Wait, I can do better than that.

Firstly think of the three scenarios available.
1. You picked box 1, the winning box. Host opens empty box 2.
2. You picked an empty box 1, host opens an empty box 2.
3. You pick an empty box 1, host opens the winning box 3.

Let's imagine he chooses randomly.
You are at the point of deciding whether to switch.
That means that of the three available scenarios, you are at scenario 1 or 2. Originally there were 3 equally likely scenarios, but we now know it isn't scenario 3, so it leaves 2 equally likely scenarios of either number one or two.

If the host always intentionally picks the empty box, then scenarios 2 and 3 merge to give the same outcome.