TITLE: Probability - A Conceptual Doubt
QUESTION [9 upvotes]: Why, when calculating the conditional probability of A given B, do we assume
that the probability of B is greater than zero?

REPLY [6 votes]: It is to avoid the divide-by-zero error that occurs when you try to divide by zero.
The definition of a conditional probability mass function, that $\mathsf P(A\mid B):=\mathsf P(A\cap B)\div\mathsf P(B)$ is only viable when $B$ has an non-zero measure.
Still, however, when $\mathsf P(B)=0$ there are other compatible definitions for conditional probability measures that can be used; although they are not necessarily probability mass functions.