Can anyone - even God - be both improbable and impossible at the same time?

Catching up on my inbox here, my friend David Rice III writes me to say, regarding the debate between Alister McGrath and Richard Dawkins on the probability of God's existence (May 30, 2007):

... Dawkins wants to have it both ways when it comes to assessing the probabilities for the existence of God. Here's how it goes..... On the one hand he said that God is not just improbable but impossible when it comes to the status of theistic EXPLANATIONS of certain phenomena (he said flat out that theism CANNOT serve as an explanation) but then he turns right around and claims that God is also an improbable being.

So that while God's existence might not be strictly-speaking impossible, theistic explanations are. But if you were to press Dawkins on WHY theistic explanations are impossible it would be precisely because God does not exist and hence has a probability of zero. So there are two different issues at play here. One is the existence of God per se and the other is the existence of the explanatory role that God provides, or has provided, for certain events or characteristics of the world. Dawkins juggles both of these ideas in the air but both of them refutes the other. If God's existence is improbable then it won't do to say that theistic explanations are impossible, they would also be improbable by extension and hence possible. But if theistic explanations are impossible then the existence of God is also impossible. It's a shell game.

But David, these people have been back-pedalling, stonewalling, and playing both ends against the middle ever since the Big Bang was first explained (1927). They need to be in a different universe. Heck, if I could make them one, I would do it tomorrow.