What does it mean for an adversary to run in PPT?
An algorithm being probabilistic means that it is allowed to "throw coins", and use the results of the coin throws in its computations. This is reasonable because a realistic adversary has access to certain pseudo-randomness sources (such as the C rand() function). Of course, a probabilistic algorithm is not required to use its randomness source (i.e., throw coins), but even if it were, it could just ignore the results.