Suppose that being over 7 feet tall indicates with 60% probability that someone is a basketball player, and carrying a basketball indicates this with 72% probability. If you see someone who is over 7 feet tall and carrying a basketball, what is the probability that they're a basketball player?

If a and b are the probabilities associated with two independent pieces of evidence, then combined they indicate a probability of:

ab + (1 - a)(1 - b)
So in this case our answer is:

(.60)(.72) + (1 - .60)(1 - .72)
which is .794. There is a 79.4% chance that the person is a basketball player.

When there are more than two pieces of evidence, the formula expands as you might expect:

abc + (1 - a)(1 - b)(1 - c)
In the case of spam filtering, what we want to calculate is the probability that the mail is a spam, and the individual pieces of evidence a, b, c, ... are the spam probabilities associated with each of the words in the mail.

For a good explanation of the background, see: