This is the name given to statistical errors that can arise when deciding the probability that a DNA sample is that of the accused. This is potentially more meaningful than usual to Troy Brown who was convicted of sexual assault and attempted murder. He has a twin brother.
This transposition of the conditional probability can produce results that range from the approximately correct to the grossly inaccurate. Without discussing the extent of the mathematical error, Mueller’s letter stated that this transposition was "so common it has been given a special name, the prosecutor’s fallacy."
Indeed, the fallacy abounds in the statements of judges, defense counsel, and journalists. Statistics textbooks, evidence casebooks and treatises, and judicial opinions all caution against it.
Court-Martial Trial Practice Blog

