Consider the following revised three-door Monty Hall problem. The contestant initially chooses Door A and Monty opens Door B, revealing no prize behind Door B. However, after opening Door B, Monty Hall also tells the contestant that, unlike the standard problem, the prize was originally placed behind one of the doors according to the following probability distribution: Door A with probability 1/3, Door B with probability 1/2, Door C with probability 1/6. What should the contestant do, switch to Door C or something else? Justify your answer with a proof