I don't see where the "basic event"/"computation of expression" distinction gets us anywhere useful. As you say, even defining it clearly is problematic, and whatever definition we use it seems that any event we actually care about is not "basic."

It also seems pretty clear to me that my mind can represent and work with probabilities smaller than 1/2, so restricting ourselves to domains of discourse that don't require smaller probabilities (e.g., perfectly fair tosses of perfectly fair coins that always land on one face or the other) seems unhelpful.