in the formula of the conditional probability, what would happen if the conditioning event be a null event?

Question

In the formula of the conditional probability,

p(a|b)=p(ab)/p(b)

what would happen if the conditioning event be a null event, i.e. p(b)=0 in the formula?

thanks.

Answer 1

A non-existent event happens with absolute certainty, so its probability is 100%, thus

P(a|b) = P(a) / 1 = P(a)

P(a|b) in this case obviously means that there is no condition at all. As a side note, you can see all three are the same in this situation:

P(a|b) = P(ab) = P(a)