You can get that the answer must be 50% once the host just reveals a goat by chance using reductio ad absurdum. Notice that since the host is doing it randomly,

You can get that the answer must be 50% once the host just reveals a goat by chance using reductio ad absurdum. Notice that since the host is doing it randomly, it would be the same if you (the contestant) were who made the revelation instead of the host. By the end both are doing it without knowledge so the results shouldn't tend to be different. For example, you could pick door 1 and then decide to reveal door 2. But in this way what you are doing is basically selecting which two doors will remain closed for the second part. I mean, selecting door 1 and then revealing door 2 is the same as picking both door 1 and door 3 at once, and then discarding the other. So, if door 2 results to have a goat, which one do you think is which should have 2/3 probabilities of having the car, door 1 or door 3? Consider that the doors don't "know" if you picked them at once or one after the other. The result would have been the same if you had first declared door 1 as your staying option and number 3 as your switching one, or viceversa. So, neither of them can be more likely than the other.