Unless I'm misunderstanding something, I don't think you'll be able to keep this with limited computational resources. All true statements will be assigned the same probability, which makes this kind of probability useless. And by hiding logical information, as you have, you are already breaking this.

No. It sounds like you imagine that the robot knows the axioms of number theory? It doesn't.

The idea is that you've got some system you're interested in, but the robot's knowledge underdetermines that system. From the info you've fed it, it can't prove all the true things about that system. So, there are things true about the system that it doesn't assign probability of 1 to. One way of thinking about it is that the robot doesn't know precisely what system you want it to think about. I mean, I've left out all facts about ordering for example, how's the robot to know we're even talking about numbers?

EDIT: however I'm realizing now that it still has to know boolean logic which means it assigns probabilities of 0 or 1 to the answers to 3-SAT problems, which are NP-complete. So, yeah, it's still got useless 0/1 probabilities that you can't calculate in reasonable time.

re: updating on computations, I have to give that more thought. It's easy to respond to clarify my thoughts, and I didn't want to keep you waiting unnecessarily, but it'll take me more time to adapt them.