You need to make some assumptions, e.g., that the room is on Earth and that "no air in the room" means a vacuum (until the smoke is introduced). Also, smoke includes both particulates and gases, so the assumption is that the gases are not significant and would not cause Brownian motion (which is what causes smoke remain suspended in air for long periods).

So, I think the most correct answer is one second. If the smoke particles don't have significant vertical motion when they are "scattered" in the room, then they would just fall to floor just like a hammer, which would take less than a second for a room that was less than few meters high. (This is because there is no air resistance, like the lunar experiment with the hammer and feather). Some of the particles may come in contact with the walls or ceiling in which case they would likely adhere to them via electrostatic attraction.

However, if any particles were near the floor and had just the right amount of positive vertical velocity, they could first move upwards toward the ceiling coming close to it but not touching it and then fall back to the floor, which would take more than a second for a room with a 3 meter ceiling.

There is also a rare scenario in which a particle could be at just the right distance from the ceiling that the electrostatic attraction from the ceiling would balance out gravity and the particle would be suspended there. However, thermal motion in the molecules in the ceiling and the particle would quickly alter the balance so that the particle would either be pulled to the ceiling or fall. I don't know if this process could take more than a second or not.

So, the most correct answer to this puzzle is "less than a second", but "less than a minute" and "less than an hour" are also correct.