P(A)*P(B|A) = P(B)*P(A|B). Therefore, P(A|B) = P(A)*P(B|A) / P(B). Therefore, woe is you should you assign a probability of 0 to B, only for B to actually happen later on; P(A|B) would include a division by 0.
Once upon a time, there was a Bayesian named Rho. Rho had such good eyesight that she could see the exact location of a single point. Disaster struck, however, when Rho accidentally threw a dart, its shaft so thin that its intersection with a perfect dartboard would be a single point, at a perfect dartboard. You see, when you randomly select a point from a region, the probability of selecting each point is 0. Nonetheless, a point was selected, and Rho saw which point it was; an event of probability 0 occurred. As Peter de Blanc said, Rho instantly fell to the very bottom layer of Bayesian hell.
Or did she?
There are mathematicians who have rejected the idea of the real number line being made of points, perhaps for reasons like this. I don't recall who, but pointless topology mght be relevant.
And happy new year to everyone.