I have difficulties with model auxiliary too.
What troubles me is the possible/probable thing
The book says may/might/could can all be used to express possibility.
But does "he may have been involved in that crime" implies possibility? Or is it a guess, which should be regarded as probability?
Can we say that 'possible' don't have anything to do with 'guess' ?
Is it true that the sentence "There may be an easier way of solving the problem" means "There definitely is an easier way"?
Or does it mean that There is a probability, say, 30% or 70%, that a easier way exists. Or..? I'm totally confused