autonav: I have two doors. One has a llama behind it, the other has an alpaca. You pick a random door and open it. What are the chances of it being a llama?
Just because there are two options, it doesn't mean they are 50-50. In my llama-alpaca example, the chances are 50-50 though because you don't have any further information. Information changes probability. If you are told that there is twice as likely chance of picking an alpaca, the chances of the llama are 1/3. If you are told the llama went sick and had to go home, the chances of an alpaca are still 1/2, but the llama is 0 ("nothing" is the other 1/2). If there are 7 doors, with 6 alpacas and 1 llama, and three doors are opened to show alpacas, you have a 1/4 of picking a llama now as opposed to 1/7 before
now if there are those same 7 doors, but you pick one, and three doors are opened (all alpacas, and the host specifically opened alpaca doors), the door you picked has a 1/7 chance of being a llama. The other three doors must sum to 6/7, and thus are worth 2/7 each, which is why, if you wanted a llama, you should switch to a different door, because you have new information.
Information changes probability