Well I want my million dollars.
So I need to engineer my belief and to do so I will need to replicate the appearance of the box several times over and borrow a million dollars.
I put the borrowed million dollars in the replicated box and open it several times a day perhaps for several months or even a few years. After a set amount of time plus some random variation a friend will switch out my replicated box and borrow million for the box omega gave me. At this point I should have every conscience reason to believe that there is more then 99% chance that there is a million dollars in the box I am opening.
Pay off the interest(if any) on my loan, pay my friend, and then find a productive use with the rest of my money.
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?