They're equally likely, but, unless Alice chose 1649271 specifically, I'm not quite sure what that question is supposed to show me, or how it relates to what I mentioned above.

Maybe let me put it this way: We play a dice game; if I roll 3, I win some of your money. If you roll an even number, you win some of my money. Whenever I roll, I roll a 3, always. Do you keep playing (because my chances of rolling 3-3-3-3-3-3 are exactly the same as my chances of rolling 1-3-4-2-5-6, or any other specific 6-numbered sequence) or do you quit?