Yes, arbitrage is possible pretty much whenever people's probabilities disagree to any significant degree. Setting P = 0 just lets you take it to absurd levels (eg. put up no stake at all, and it's still a "fair bet").

When you're saying that this doesn't solve Newcomb's problem, what do you expect the solution to actually entail?

Maximizing the money found upon opening the box(es) you have selected.

If you like, replace the money with cures for cancer with differing probabilities of working, or machines with differing probabilities of being a halting oracle, or something else you can't get by exploiting other humans.