The last may seem a bit vague, and it is hard to pin it down completely, but as a general guideline, try to make each sentence count. Paulos has, in my opinion, confused these two probabilities by his reference to guilt in the second paragraph. The probability of an event is the long run frequency of its occurrence. Two events are independent if the occurrence of one does not make the occurrence of the other more or less probable. If two events are independent, the probability of both of them occurring can be calculated by multiplying.
Events are often dependent.
When events are dependent, the probability of one event, say A, given that the other event, say B, has occurred, is now the frequency of occurences of A among situations where B has occurred. This is usually a small, even tiny, probability. The key to computing one conditional probability from the other one is Bayes theorem. But it extends readily to more than two events. The probability of a DNA match given the defendant is guilty is usually taken to be 1.