There are lots of theists who understand probability theory and who consider themselves "rational" or even "rationalists".
Yes, but in the matters of faith they start with the bottom line, and make up the relevant probabilities along the way to match it.
Sometimes, but they're not aware that's what they're doing. So in practice that probability is irrelevant, but I'm pretty sure that in practice Richard Dawkins is never going to assign a significant probability to "God exists". He still assigned a not-zero probability when asked. Same with such theists.
Other times, they're genuinely quite rational people who have literally never heard of most of the evidence and arguments against their position. I once saw a theist renounce their faith after an hour of real debate, because that was just the first...
http://bigthink.com/think-tank/neil-degrasse-tyson-atheist-or-agnostic
Apparently Dawkins and Tyson give a non-zero probability to "God". Which is pretty much what is expected of a rational person. And of course it will be used by theists to say "They aren't really sure!"