You start with a 66% chance of choosing a goat. The host opens a door and shows a goat. If you switch, you turn that 66% chance of choosing a goat into a 66% chance of choosing the prize. The fact that the host knew or didn't know what was behind the door is irrelevant.
Also, if the host opened the door with the prize, what would happen then?
Also, if the host opened the door with the prize, what would happen then?