You do not want the probe to be inside on the floor. If it is moved, flooded by water, or flooded by urine the probe will send the tstat the information that it is cold and needs more power. This of course is wrong and will make the uth ramp up and get to hot, possibly hot enough to harm your snake.
You want to mount the probe to the heat mat itself and have both outside the cage.
Most cages will have small feet that act as spacers. This allows your heat mat and probe to sit under the cage without any issues. You want to mount the heat mat directly to the bottom of the cage tightly with tape of some sort. I like the aluminum A/C tape. Its rigid, tough, and heat tolerant.
If the cage does not have space under it and instead sits flat on the surface below you can use the small rubber inserts usually used to place glass on top of table stands or other table tops. Cheap and easy.