Yeah this is it I think. If I can restate more simply for the 3-door case: You pick. The doors are now in two groups: your door (1/3 chance) and the other two

Yeah this is it I think. If I can restate more simply for the 3-door case: You pick. The doors are now in two groups: your door (1/3 chance) and the other two doors (2/3 chance). The host picks. The second group is now reduced to a single door, still with 2/3 chance. Now you decide - stick with the door with 1/3 chance, or switch to the door with 2/3 chance?