Yes, this is a standard incomplete information problem. Yes, you can do the calculations at any convenient time, not necessarily before meeting Omega. (These calculations can’t use the information that Omega exists, though.) No, it isn’t quite as simple as you state: when you meet Omega, you have to calculate the counterfactual probability of you having met Upsilon instead, and so on.
Yes, this is a standard incomplete information problem. Yes, you can do the calculations at any convenient time, not necessarily before meeting Omega. (These calculations can’t use the information that Omega exists, though.) No, it isn’t quite as simple as you state: when you meet Omega, you have to calculate the counterfactual probability of you having met Upsilon instead, and so on.