The best, and clearest, explanation of the problem that I have read is, of all places, in a novel entitled "The Curious Incident of the Dog in the Nighttime" by Mark Haddon.

HOWEVER - Haddon's explanation, and all the others that I have read, seem to assume (tho' not state directly) that Monty would offer the choice no matter which door the contestant had initially selected.

But what if Monty offered the choice ONLY if the contestant had initially chosen the door with the car? Would that change the percentages?