For any state of information X, we have P(A or not A | X) = 1 and P(A and not A | X) = 0. We have to have 0 and 1 as probabilities for probability theory even to work. I think you’re taking a reasonable idea—that P(A | X) should be neither 0 nor 1 when A is a statement about the concrete physical world—and trying to apply it beyond its applicable domain.
For any state of information X, we have P(A or not A | X) = 1 and P(A and not A | X) = 0. We have to have 0 and 1 as probabilities for probability theory even to work. I think you’re taking a reasonable idea—that P(A | X) should be neither 0 nor 1 when A is a statement about the concrete physical world—and trying to apply it beyond its applicable domain.