its 67% chance of winning because the host has knowledge of which door had the winning prize behind it and which had the dud and is forced to open the door with the dud.

Consider this. After your first decision there are only three possible outcomes.

You chose the prize right the first time.

You chose dud 1.

You chose dud 2.

Since a dud must be removed by the host. Its easy to see that by switching you increase your chances of winning (the only way you could switch and lose is if you picked the prize the first time, if you chose either dud the first time you'd be better off switching)

The following is a list of all possible outcomes of the game
D = first choice is dud
P = first choice is prize
S = switch
NS = no switch
W = win
L = loss

D-S-W (first dud)
D-S-W (second dud)
P-S-L
D-NS-L (first dud)
D-NS-L (second dud)
P-NS-W

As you can see, by switching, you attain a 67% chance of winning the game.