The cloudkill spell creates a "20-foot-radius sphere [...] centered on a point you choose within range", spreads around corners, and
moves 10 feet away from you at the start of each of your turns, rolling along the surface of the ground. The vapors, being heavier than air, sink to the lowest level of the land, even pouring down openings.
So yes, it'll trace along the floor, whatever the floor does, including dropping down into a hole.
My interpretation of this is that the 'pouring down openings' thing is meant to indicate that it doesn't need a 40-foot opening to move around. The sphere doesn't roll across the landscape like a ball, but rather the center-point runs along the surface of the ground, following the terrain, and the fog fills as much of that twenty-foot area as it can.
So if you had the sphere approaching a very deep pit and the center-point ends its movement right on the lip of the pit, you'd have a nearly complete sphere of fog centered on the edge of the pit, then the next turn the center will move 10 feet straight down along the wall of the pit (or freefalling if it's like just a hole in the middle of an unsupported floor) and continue to fall at 10 feet per turn until it reaches the ground.
Instead of thinking of the cloudkill as a cohesive ball of fog, I'd think of it as constantly being produced by the centerpoint and evaporating at the edge of the area of effect.