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.
"Your confidence that there's a million dollars in the box" does not uniquely identify a value, even at a single point in time. The mind has more than one method for representing and calculating likelihoods, some of which are under conscious control and may be overridden for game-theoretic reasons, and some of which aren't.
These are technical issues with the hypothetical, irrelevant to its intended sense.
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?