I've worked it out. There is a prize behind only one door, so initially your chances of choosing the right door is 1 in 3. However an incorrect door will be removed, and you'll have a choice to swap doors. This means that there is a 2 in 3 chance you will choose the correct door if you swap after a door has been removed.

To put it simply:

1xGood Door, 2xBad Door

Chance of choosing good door is 1 in 3, chance of choosing bad door is 2 in 3.

You are given the option to swap, if you do you push the odds into your favour because there is a 2 in 3 chance you will swap to the good door.

Possible outcomes not swapping (X is bad, Y is good):

1.
X X Y
^

(Loose)

2.
X X Y
   ^

(Loose)

3.

X X Y
     ^

(Win)

= 1 in 3 chance of winning.

If you swap:

1.
x X Y
^
to
x Y
   ^

(WIN)

2.
x X Y
   ^
to
X Y
   ^

(WIN)

3.
X X Y
      ^
to
X Y
^

(Loose)

= 2 in 3 chance of winning. I'll post back when I have a riddle, that was a rather tricky one.