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?