Consider a crime where some DNA is found.

Case 1)

The police, using other evidence, find, arrest and charge someone with the crime. Then they test his DNA, and find it matches. The chance of a wrong match are approx 1 in a million, and the this evidence is brought to court; the jury convicts on the basis of it.

Case 2)

The police have no evidence whatsoever, except for the DNA, and so they look this up in the database. They find a match, and arrest the man. The same statistics are given to the jury, who convict.

The Bayesians reading this will spot the subtle flaw; most police and jurors will not. The flaw is this: in (2), we have already "used up" the information given by the low probability of a mismatch when we searched for the suspect. [Out of a population of 50 million, it's almost certain that someone in the database will match] We can't then use the *same* DNA statistics to prove guilt "beyond reasonable doubt".

This is why DNA databases are dangerous.