It's likely in either the throne, the ceiling, or the Ophiuchus dorms beneath the arena.
During the game, someone will case the area on another pretext to determine the location for sure. Then Orion, Pyxis, and Canis will cause a distraction while Scowl, cloaked so that King can't spot him, takes it and runs. Even if it's the ceiling, he should be able to reach- those shoes he wears let him jump to heights that simulate flying, and they grant him the speed to clear the area quickly afterward, too.