June 2009 (UTC)

I wouldn't speak of "consistent way" to treat the problem. The placement of the car to be random seems quite natural. The distribution of the initial choice of the player is unimportant for the problem and is not specifically considered to be random. The  strategy of the host is considered to be random in the MHP and doesn't take away the necessity of the conditional probability to be considered. Only for the sake of showing the dependency of the host's strategy it is varied, as any mathematician would have done. So, I'm sorry, I do not see your point.   13:38, 4