This is where context, and the challenge of having meaningful consequences to ability checks, matters.
If you are talking about who gets to check if they recall some lore, I think that illustrates the problematic nature of resolving those things with ability checks, and why I don't like to use them.
If you are talking about who gets to try to pick the lock before the guard finishes the circuit, with a failure attracting attention, then it's up to the players to decide who is going to try.
If you are talking about who gets to try to jump over the lava, heck anybody who wants to can give it a shot. (Mwuhahahahaha)
The larger point being that if consequences are defined, the DM doesn't have to made decisions about who gets to try.