No. Do not put the probe inside the tub. If you were to place the probe inside the tub it could easily be moved, urinated on, or flooded by water which would make the tstat thing the tub is cold and ramp up the heat source causing the heat source to over heat the tub and put your snake in danger.
Its is completely normal to have different temps read at the tstat probe and the cage floor. You lose some heat as it travels through the materials so the tub floor should be a little cooler than the heat source.
Also measure the temp directly on the tub floor and not on top of the substrate. The substrate should be thin over the heat source as well, 1/4 inch works well.
NOTE- NEVER use tape inside a tub, tank, cage, anything where the snake can reach it. It can really harm your snake.