Of course, if you call fopen with uniformly distributed random filenames then it is extremely unlikely than such files will exist. Thus it will fail with probability essentially 1. Yet, I don't want my programming language to force me to make an asymmetric distinction between the two cases.

By "equally likely" I don't mean "having equal probability to occur". This is very difficult to model, and it will depend mostly on the usage patterns of the users of the program. I mean that both cases are worth of the same attention and merit an equivalently serious treatment. No need to disparage one of the two cases as an "error" or an "exception" and require a special language construct.