I think there is good reason to believe that the population divides into a large majority who have never done this and a very small minority who have done it repeatedly. You would be right in general, but with such a bimodal distribution the correlation goes both ways. If most of the people who have ever done it have done it several times, and hardly anyone else has done it at all, then the odds are small that anyone you catch is doing it for the first time.
I think you also need an assumption that the criminal population is not growing (or is growing sufficiently slowly). Of course, that also seems plausible.
