It didn't get any more intuitive for me like that. If anything, less. When it clicked for me is when I thought of it as being 1/3 probability the car is behind

It didn't get any more intuitive for me like that. If anything, less. When it clicked for me is when I thought of it as being 1/3 probability the car is behind your door, and 2/3 it isn't. That doesn't change whether they show you one of the other two doors or not, so switching to the 2/3 option is better.