P(H | E) = P(E | H) P(H) / P(E).
In words: posterior is proportional to likelihood times prior.
The practical technique for interviews is to abandon percentages and use natural frequencies. Imagine 100,000 people, count how many land in each cell, and take the ratio. The arithmetic stops being confusing almost immediately.
The trap. The base rate dominates when the event is rare. A 99%-accurate test for a 1-in-1,000 condition yields a positive result that is genuine less than 10% of the time, because false positives are drawn from a vastly larger population than true positives.