I think that’s a bad example, as classifiers tend to output a floating point number and you use some threshold/activation function to collapse the classifier into a particular state. In that sense there is nothing qualitatively different when the classifier outputs 0.85 vs 0.87.
That’s interesting right? The distribution by itself doesn’t provide the structure required. You need an activation function (idk what the term of architecture for this is in ML) to impose some sort of semantic structure on top of the distribution (eg softmax)