the mean free path of molecules is comparable to the size of the equipment. The gaseous phase no longer exerts significant pressure on the substance to be evaporated, and consequently, rate of evaporation no longer depends on pressure.
The average distance a molecule travels before colliding with another is comparable to the size of the apparatus. In the gaseous state, the equipment's pressure has little effect on the substance being vaporized, so the evaporation rate isn't affected by pressure anymore.