Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 17 / c / iii / Solution

The numerator $P(B\mid A)P(A)$ equals $P(A\cap B)$, while $P(A\mid B)=P(A\cap B)/P(B)$. Thus, wherever the original quotient is defined,In particular a zero numerator and denominator cannot be cancelled; the original expression requires $P(A\mid B)>0$. This is the rearrangement of Bayes' theorem.