The fact that Montey only reveals a goat is key to the probability calculation. When the player selects a door, they have a 1/3 probability that they have chose

The fact that Montey only reveals a goat is key to the probability calculation. When the player selects a door, they have a 1/3 probability that they have chosen the correct door, and Montey has a 2/3 probability of having the car. When he reveals the goat (which he always had behind one of his doors) that 2/3 probability shifts to the remaining door. There is no chance in Montey's selections, he knows where everything is to begin with.