As promised, an entire post dedicated to asking whether or not the phrase "There probably isn't a God" can be scientifically justified.
I'm sure for some people, there seems no need for such a thing. Garathon, who sent me the link to Christian Voice's objection, mentioned that this was a conversation best had over a pint of Carlsberg. Assuming he hasn't just become a raging alcoholic, his point is clear: if Carlsberg can claim to be "probably the best lager in the world", then arguably the ASA have already made their decision regarding whether or not such things need to be proven.
Since I'm a sucker for a good intellectual question, though, I'm more interested in the extent to which the phrase is or isn't accurate.
We can dispense with the consideration of "probably" pretty easily. An event described as probable must have more than a 50% chance of occurring. Some would say that it would need to be a little higher (to get us out of the dreaded "maybe" zone), but I would not object to the word's use in describing anything more likely than not occur; and this is my profession, so I get to make these calls. It is also arguable that the phrase has an upper probabilistic bound also, but that doesn't really concern me. Anyone arguing that "probably" doesn't go far enough (as some have, including, inevitably, Dawkins) tend to be working from a specific image of God (most commonly Judeo-Christian, but certainly one that predates the universe itself) that I don't think we need to limit ourselves to.
Thus, the question becomes: can we say that God is more likely than not to be fictional? Part of the problem here is that when we discuss probability, we usually do so in the context of events occurring which have occurred before, or which are sufficiently similar to others that have occurred before as to make discussing them fairly simple. For example , having decided the chance of rolling a 6 on a fair die is one sixth, we have no trouble extrapolating that rolling a 5 on it will have the same chance. It's a similar enough event that we understand how to extend our thinking to it. Similarly, if our die is replaced with another one, as identical as the universe will allow, we will happy assigning a probability of one sixth to rolling a 6 on that die, too.
Thus, probabilists deal in considering repeats (or slight variations) on previously observed phenomena. We're not really in the business of trying to assign probabilities to events that have no similarity to observed phenomenon. Obviously, some things that seemingly cannot be linked to other events can be considered from first principles. Consider Shrodinger's cat, for example. If one were asked to give a probability that the cat is still alive, one could dig out information about the average life-span of cats, or even attempt to model probabilistically the release of radiation (which may in fact be physically impossible, though last I checked the jury was still out), and make a judgement based on that.
But now imagine you've never heard of a cat. You have no idea what it is. It may not even be of this planet. All that you know is that it is a life-form that will be killed by the flask in the box. How can you possibly attempt to assign a probability to the event now?
Imprecise probabilists concern themselves with this sort of stuff quite a bit, but that's another conversation (a very long and boring one, which will make many of you cry). What's important is that being asked to adjudicate on the probability of God's existence is made incredibly difficult by the fact that not only is direct equivalence impossible, but attempting to use first principles is really difficult. If we were capable of understanding how every sub-atomic particle interacts with every other, it might conceivably be possible to predict radiation, but it's not at all clear that even such total understanding of the basic building blocks of reality would give us any more to go on regarding the existence of God (though in a real sense we might then consider ourselves omniscient and in some sense become God, but that's a thought that hurts my head).
What do we have left? Well, according to Clifford Longley, there are two possible ways to proceed. One is "eye-witness testimony" from all those that have witnessed miracles, or even spoken with God personally. The second is to appeal to the "fine-tuning" of the universe (which assumes the same thing as Dawkins has above, that God=Creator).
The problem with miracles, of course, is that so many religions lay claim to them. If we assume that there genuinely have been events that have taken place that have defied modern science (and defying science isn't the same thing as baffling it), then why are they spread over so many faiths? God seems a little arbitrary in the flexing of his metaphorical muscles. It's possible, as some have argued, that God doesn't care how you say your prayers, so long as you say them. Once you start thinking along those lines, though, why does God need to be involved at all? If there's no reason to assume God is sending a specific message to specific people (rewarding the devout, demonstrating his power), then all that's left is an event that is contrary to our understanding of the universe. Assigning that event to God is no more or less valid than blaming thunderbolts on Thor. As science advances, the list of events that are inexplicable or theoretically impossible constantly changes; to take a snapshot of current understanding and claim that those things that lie outside but still happen must prove God is massively dubious.
Similarly, the idea that God talks to people is somewhat problematic. First, people have also claimed to talk to fairies, mermaids, and the ghost of Napoleon. Secondly, there are any number of medical conditions or outside influences that can be confused with hearing the voice of God. Thirdly, and perhaps most importantly, much of religion works on the principle that faith is something that has to exist without proof. "Proof belies faith, and without faith I am nothing", as God Himself said in the Hitchhiker's Guide. But if the Babel Fish is a dead give-away, then actually showing up in person for a chat must be even more of a blatantly unsubtle clue. This works for miracles as well. As far as I can see, God wants us to believe in him, or he wants us to be aware of his existence as a fact. I don't understand the argument he can want both at once. Certainly, if he does want that, then he's to blame for the bus campaign in any case and Christian Voice needs to spend some time trying to be Christian Shut The Hell Up. 
Whilst we're referencing Douglas Adams, it's worth mentioning the puddle analogy I first read in The Salmon of Doubt. For those who haven't heard it, it goes roughly along these lines. A puddle is amazed that it's inside a hole that's just deep enough to contain it, and just wide enough as well. Not only that, but the bottom of the hole fits the contours of the puddle's underside exactly. Given all of that, the puddle sees no option but to conclude that the hole was specifically designed for it.
It's a far better rebuttal of the "fine-tuning" argument than I could ever manage. Looking around at a universe that, were any of thousands of physical properties to vary even slightly, could never have produced us or anything like us, it is tempting to believe that this confirms the universe was designed for us, and thus that God exists. Someone once referred to this as "proof by lack of imagination", since inherent in the argument is the assumption that human or human-like life is the only possible arrangement of atoms that could be considered alive. Changing the rules might render our existence impossible, but maybe some other lumps of matter would be looking around instead. Assuming matter still had any meaning. Or atoms. Or looking.
You get the idea. I've touched on this before, but since every aspect of our understanding and reasoning is based on what we can observe in this reality, attempting to imagine others is incredibly difficult. All of which makes the "fine-tuning" argument difficult to swallow, even before it's pointed out that there may be other universes, either parallel to us, or before us (again, assuming "before" means anything in this context), and therefore thinking the universe is suspiciously well-designed is just as foolish as me being suspicious that the trillions of potential combinations of spermatozoa and eggs that could have intersected whilst my parents were trying for a baby (not that this is a subject I'm particularly keen on thinking about) somehow produced me.
In short then, I don't believe there is any evidence for God. Evidence requires scientific, unbiased observation and experimentation, and neither of the above qualifies. Of course, since proving the non-existence of God is also impossible by direct observation (though specific Gods might be ruled out, we're certainly past the point where we need Thor, for example), it may appear that we've ended up in stalemate.
Is that really the case, though? If we cannot observe God, then our only alternative is to employ reason. Whilst it is true that the idea of multiple universes is currently no more verifiable than God's existence, it does at least skip the thorny problem of increased complexity. Pointing to the universe's balance and claiming this proves God is solving one problem by creating another, far more complicated one. It is an anti-explanation. In order for God to exist, any number of questions appear that need answering, that otherwise wouldn't exist.
Given that, then, given "God exists" is a hypothesis with no evidence for or against, but which fails the test of Occam's razor, I think "The probability that God exists is strictly less than 50%" is a drastically oversimplified statement (I would expect to be torn to pieces by my supervisor were I to say it to him, and not just because he is a devout Catholic), but, if one were to write all probabilistic statements regarding God at the same level of simplicity, then this would be the most plausible.
 For those up on their probability theory, I am going to assume that we can use "objective" probabilistic judgements, purely because doing so won't really affect anything in the context of this discussion, and so as not to confuse the crap out of people.
 The sad corollary to this line of thinking is that I must believe that everyone who claims to have spoken to God personally is lying, or mistaken. Which, much as I don't tend to bring it up at coffee mornings, is in fact the case. Sorry.