I did do a quick simulation but I have just done it again more thoroughly, and this time got 35%+/- 1%. Sorry about that, chief. It may pay to do your own.

As a rough guide, there are about 500 chances, each of which is about 0.001 so the expected number is 0.05. If you approximate with the poisson distribution you get p(1 or more triple) = 1 - e^-0.05 which is about 39%