The Prosecutor's Fallacy

The field of statistics has quite a few types of fallacies up its sleeve. The prosecutor's fallacy is a particularly misleading one. In the courtroom, the prosecutor may not purposely use the fallacy to present evidence. Neither may the defense, who might use it to argue a suspects innocence. Still, sometimes the fallacy is presented by mistake.

Let's say some DNA is found on a murder scene. The police have a DNA databank containing 20,000 people and run the sample through it. There is a match, the suspected murderer is identified and put to trial.
The crime scene analyst testifies that the probability of two DNA profiles matching erroneously is only 1 in 10,000. The jury concludes that this means that there is only a 0,01% chance that the suspect is innocent.

Would you conclude the same?