Are you really sure there's no bacteria there? Unless you absolutely drench it in alcohol, there are very good chances something will survive. Even the meat itself it's going to be completely sterile unless it's burnt to a crisp. And ask yourself about other things, what did you use to transfer the meat to the drawer? Doesn't matter if it's only a couple cells that survive, they will immediately get to work on the steak and soon you'll have an entire colony.

And yes, they can also be blown about by air currents and land on the steak, they can do without food for a couple of minutes.