Richard Dawkins argues that the probability of God's existence must be very low (but not zero):

Accepting, then, that the God Hypothesis is a proper scientific hypothesis whose truth or falsehood is hidden from us only by lack of evidence, what should be our best estimate of the probability that God exists, given the evidence now available? Pretty low I think...

Dawkins appeals to multiverse theory to explain why things having very, very low probability (but quite necessary for life) have occurred:

[In The God Delusion] Dawkins now introduces the ‘multiverse’ theory, which says that beyond our universe there exists perhaps an infinite number of other universes, each having a different variation in the laws of nature.

According to Dawkins, God is improbable -- but so also are aspects of this universe. If it's legitimate to pose an infinite number of universes to make improbable events probable -- or even certain (by increasing the total probability space) -- then the probability for God must also increase accordingly (as the space in which he can occur is also increasing), also thus arriving at near certainty.

Further, Dawkins believes if God existed, he must have required time to evolve:

Complex, statistically improbable things, by definition, don't just happen; they demand an explanation in their own right. They are impotent to terminate regresses, in a way that simple things are not. The first cause cannot have been an intelligence - let alone an intelligence that answers prayers and enjoys being worshipped. Intelligent, creative, complex, statistically improbable things come late into the universe, as the product of evolution or some other process of gradual escalation from simple beginnings.

So God could have been produces as the result of time in some kind of universe, and there are a huge or infinite number of universes, then one of them almost certainly should have produced a God of the kind required to make this one.

I agree, this isn't a "proof" of God's existence, as it only shows that, by Dawkins own rules, and his new appeal to multiverse theory, he must now also admit that the has made the probability of God very high. If "very low" probability is sufficient grounds for Dawkins to disbelieve in something, then "very high" probability must also be sufficient grounds to believe in it.

So by Richard Dawkins own logic, he should be now quite open, if not nearly positively sure, that God almost certainly must exist.