Why is the definition of Special-honest verifier zero-knowledge probabilistic?
The probabilistic nature is not specific to special-honest verifier zero-knowledge but that's what zero-knowledge is about. With zero-knowledge you want to formulate that such an interactive proof does not leak any 
information besides the validity of the claim, as it is efficiently simulatable meaning that real and simulated transcripts are not distinguishable. 

That a simulator produces accepting transcripts does not necessarily mean that this simulated transcript cannot be distinguished from a real interaction. Assume for instance an artificial simulator that always uses the same $a$ independent of the value $e$. So the transcript could be an accepting one, but one could distinguish transcripts coming from real interactions and simulated ones.