May and can

This all started with a small incidence narrated by one of my friends, Mohan, When I was in ADA. The narration was like this:
Somebody called his freind over phone asking,"Can I speak to Mr.Vijay"(name changed)
and his friend answered,"you can, but you may not!".
That time(when this narration was made), I was a 'buchcha' in this type of sensitive english. So, I simply remembered.(Many times I do this. I simply remember the things that I dont understand, hoping to understand them somewhere in the future).
Later, I dont know when, at some point of time, I got to know the difference. Some day while discussing with Phani, I began elaborating him, "you can hit your boss with a stone in public, but you may not", which makes it pretty clear. 'Can' is the matter of capability and 'may' is the matter of probability.
And that exactly made me understand this:"after removing all that is impossible whatever remains however improbable must be the truth". This appears in one of the short stories written by Sir.Arthor Canon Doyley.(This sentence, I might have gone through, while reading Sherlock Holmes stories, but didnt realize the meaning at that time)
Once I understood the meaning of this, the revelation for me was tremendous. Bacause, gradually, as I recollected Sherlock Holmes stories, I found that, each of the analysis that Mr.Holmes conducts for his deductions is based on this particular principle. Though this basic principle of detective work can be put so simple, there still remains a great challenge for the detectives. That is, to demark between what is impossible and what is improbable. Because this demarkation greatly depends on amount and accuracy of information, the detective holds.