Initial pick: 1/3 chance of winner

Question: did you pick the correct door?

  - If correct, both remaining doors are losers, eg. {loser, loser}.   
  - Otherwise, the remaining doors are {loser, winner}.
    And the loser must be revealed according to the game rules.

If you don't change your answer, you're stuck with the initial chance: 1/3

If you change your answer: (1/3) * 0 + (2/3) * 1 = 2/3

  - (1/3) you initially picked correct, then change to a guaranteed loser.
  - (2/3) you initially picked incorrect, then change to a guaranteed winner.