How exactly is your "belief" probability determined? This seems like one of the cases where lumping everything as one "belief" does not work.
If you ask for verbal declarations or betting odds, the belief will come out over 99% even if it doesn't feel right.
The subjective anticipation is a different part of your brain, and it doesn't talk in probabilities - you'd need some sort of rough correspondence between strength of anticipation and observed frequencies or something- and I'm not sure how well even that would work.
Like James Miller said, this is a lot like the placebo effect when told that its only the placebo effect. It seems like people can make that work, but that there are complications (say it as if they wont believe in it strongly to work- or that they'd be fooling themselves and it likely wont work. Say it as if it will work and it's virtuous for it to work, and it probably will).
I came to the comments section to make this exact post.
Omega appears to you in a puff of logic, and presents you with a closed box. "If you open this box you will find either nothing or a million dollars," Omega tells you, "and the contents will be yours to keep." "Great," you say, taking the box, "sounds like I can't lose!" "Not so fast," says Omega, "to get that possible million dollars you have to be in the right frame of mind. If you are at least 99% confident that there's a million dollars in the box, there will be. If you're less confident than that, it will be empty. I'm not predicting the state of your mind in advance this time, I'm reading it directly and teleporting the money in only if you have enough faith that it will be there. Take as long as you like."
Assume you believe Omega. Can you believe the million dollars will be there, strongly enough that it will be?