I like that. I started playing by twiddling P(A). Since probabilities add to one, there are only three degrees of freedom. I got that the other two degrees, P(B|A) and P(B| not A) didn't move, why would they? By contrast P(A|B) and P(A| not B) in the other column did move - so far so good.

But P(B) just sat there. Puzzling. Then I realized that it starts at P(B|A) = P(B| not A) which is a special case.

An excellent philosophical toy :-)