Spoiler Below There are 3 possible situations.
(Case 1) Monty picks door 1.
This has a 2/3 chance of happening, & once it happens, your odds for switching are 2/3 by the original Monty Hall problem, since opening door 1 reveals nothing conclusive about doors 2 & 3.
2/3*2/3 = 4/9
(Case 2) Monty picks door 2 (1/3 chance of happening), & you had already picked door 2 (1/3 chance of happening).
You should switch to door 1 right now, 100%.
1/3*1/3*1 = 1/9
(Case 3) Monty picks door 2 (1/3 chance), & you had already picked door 3 (1/3 chance).
Again, switch to door 1, 100%.
1/3*1/3*1 = 1/9
(Case 4) Monty picks door 2, & you had already picked door 1.
The car is behind door 1; stay put.
Odds for switching = 0.
Total: 4/9+1/9+1/9+0 = 6/9 = 2/3.
And remember, "I'm-a Luigi, number one!"