For example, how do I refer to the top three or four participants in a tournament. The victorious doesn't apply; would finalists be the best choice here?
The term leaderboard is often used
A scoreboard showing the names and current scores of the leading competitors, especially in a golf tournament.
The term may be used somewhat figuratively, even where there is not a public display of rankings, as in Where do you stand on the leaderboard?
Favorite - a competitor judged most likely to win.
So "favorites" should mean the competitors most like to win or liked by people. Unless you provide more context, as to what you are really referring to, "favorite" fits.
Also, you can call them "bellwethers," plural for "bellwether" which means the one that takes the lead or initiative.
The definition is from merriam webster.
Is your "top three or four" an arbitrary small number out of all the contestants or are you talking about the specific number of people who receive medals?
You could split it into "first place" and "runner-ups", which would include the several top contestants who do receive some sort of prize or recognition.
"Semifinalists" can be used in a bracket tournament to refer to the final four contestants, but can be only used before the final match takes place.
"Contestants in the final round" might be appropriate if your competition is round based and the last round has 3 or 4 people. Or at least a small amount of people such that being in the final round is seen as some kind of accomplishment (American Idol, spelling bee, etc)
"Contenders" or "remaining contenders" is commonly used.
Once someone's out of the tournament, they're no longer in contention for the prize, so they're no longer a "contender". "Remaining" emphasizes that you're only talking about the ones still in the tournament.
Other events use the current tier, and refer to them as "quarter-finalists", "semi-finalists", and "finalists" when they're in the round of 8,4,2 respectively.