I feel like you're fighting the meaning of the word given here. You might as well say that your probability of winning is tiny because you're unlikely be picked

I feel like you're fighting the meaning of the word given here. You might as well say that your probability of winning is tiny because you're unlikely be picked as a contestant, or even less likely than that because you might live somewhere than the US. The whole premise of the problem is that you are already on the show looking at an open door with a goat behind it.