The way it has always been explained to me is that everything goes outside the tank, under the glass floor. The probe is sandwiched between the UTH and the glass; all this is taped to the glass under the tank, and is therefore safe from accidents like a spilled water bowl, or the cord getting pulled out by an active snake.
Glass insulates/dissipates a little bit, so the temp on the floor inside the tank will be about two degress lower than what the T-stat is set for. You will want to probably need to set the t-stat one or two degrees higher than what you want for the snake.
The probe does create a lump, so the pad doesn't lie perfectly flat, but I just use tape all around the edges. I back the taped on UTH with foil and some small scrap sheets of styrofoam for insulation. I found, at least with the standard aquariums, that the cords running out from under the tank necessitated adding feet under each corner of the tank to stabilize it. Otherwise, one could just add more sheet foam underneath the whole thing, and raise the lower rim of the tank that way.
I was not able to set up the large Exo Terra that way. This glass house is just too big to lift safely alone, so I set up the UTH and probe on the floor inside. Not ideal, and needs refinement. I ordered a replacement probe for the t-stat, and plan to silicone the UTH pad, the probe to a foam bottom so there is no danger of them getting wet, or pushed apart. I'll add a small thin sheet of slate on top, and see if that will make a good hot spot for the warm hide. Still a work in progress.