@dalehileman,
Quote: "the" okay, especially if there were other specific instances of judging to which I'm comparing myself
Right, it all depends on context. Say, for example, you were at a poetry reading exhibition where the winner (by declaration of the judge) would get a prize. After a given recital someone, apparently mistaking you for the judge, comes up and asks: "Is that one going to win the prize?" Then "the" would be appropriate. I might be the judge for the upcoming prose presentations, but not of the poetry sessions, ya know?
The only answer that would never be right is "an." Given the most common and frequent circumstances "a" would be most typical. But "a" is not THE right answer for all contexts.