Via The Big W:

The false positive paradox is a statistical result where false positive tests are more probable than true positive tests, occurring when the overall population has a low incidence of a condition and the incidence rate is lower than the false positive rate.

In other words, if the incidence of steroid use among Major League ballplayers is lower than the test's false positive rate, a majority of players who test positive will, in fact, be clean.

There's obviously a lot we don't yet know about the Braun case, but I suspect this information might be useful in the coming days and weeks.