<i>But I thought we were talking about the difference between the following two scenarios:
1. Host knows where the prize is, and always opens a door without the prize. (Which will always exist).</i>
In this case, your host algorithm always chooses the empty door, thus producing 66% chance for the prize to be behind that door.
<i>2. He opens one of the remaining doors at random. The prize happens to not be behind the door he opened.</i>
In this case, your host algorithm chooses the door with the prize in 1/3 of cases. You will exclude those cases after running the algorithm (always choosing the empty door would correspond to host knowing and would thus alter the result of the algorithm). This will result to cases where the host opens the second door being less frequent, thus bringing the probability to 50/50, as all doors are as probable in this case.
<i>In those two cases you're better off switching.</i>
The change in probability of changing doors in latter case arises from the host altering the likelihood of an event which is less likely in a truly random situation. If you initially choose the wrong door, it is only 50% likely that the host opens an empty door for you in a true random case. If the host knows, then the chance of host opening an empty door is 100%, no matter what. In a true random situation, there is two cases where the prize is behind your door for every one case where it is behind other door, with the one case being twice as probable as the two. Thus, the odds are (25+25=50)/50. Thus the other door does not become more probable, as the host is not manipulating the likelihoods in a true random case.