The same 50/50 analysis seems to apply. (Though I've been wrong before!
Assuming I understand the rules this time:
1/3 of the time your initial pick is correct; Host 1 always a Jack; you lose when you switch.
2/3 of the time your initial pick is incorrect, but half of those times don't count since Host 1 shows the Queen; for the half that do count (2/3 * 1/2 = 1/3 of the initial starts), Host 2's actions change nothing and you win when you switch.
So, it's fifty-fifty!