It's not a Sherlock Holmes case at all. That principal only applies to locked-room style mysteries, with a provably tiny pool of possible suspects that can be eliminated one by one. I.e., fictional situations.
In this case, the set of "other possible suspects" includes literally everybody in the world who loosely fits the description of the killer and can't prove they were elsewhere that day.
In this case, the set of "other possible suspects" includes literally everybody in the world who loosely fits the description of the killer and can't prove they were elsewhere that day.