The remaining doors are not random. The one you picked still has a 1/3 chance of winning, that doesn't change with opening another door. However switching doors is essentially the same as picking all the other doors at once, since the door with a goat is not opened, thus the 2/3.
Imagine the thing with 100 doors and imagine the host isn't opening any doors, but just telling you what's behind them and it becomes pretty obvious.
Imagine the thing with 100 doors and imagine the host isn't opening any doors, but just telling you what's behind them and it becomes pretty obvious.