Modeling electrons as tiny objects that have probability distributions has a weakness. There is no sensible value to assign to the 'tiny'. I mean there is no experiment to determine the 'size' of the electron.
That's essentially just an approximation. In some problems it can be useful to model the electron as having a finite radius, but our current understanding is that particles like electrons are literally infinitesimal points. In that case it's generally more useful for us to use things like Dirac delta functions to model them more accurately.
Check all the disclaimers on that concept, in particular "Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic"
