It does not go inside the tank.
1. If the probe gets moved from where you have it set up the tstat will think the uth is not hot enough and crank up the power. This will make unsafe temps in your tank and put your snake in danger.
2. You snake could urinate on the probe location causing the tstat to think the uth is not hot enough and crank up the power. This will make unsafe temps in your tank and put your snake in danger.
3. The water bowl could be flipped causing the tank to flood which will make the tstat will think the uth is not hot enough and crank up the power. This will make unsafe temps in your tank and put your snake in danger.
You see the pattern?
Place the probe outside the tank between the uth and the bottom of the tank. The common way to secure it is foil tape, hot glue, or duct tape. If I remember correctly the tstat you have has a huge probe. Some have found putting the it between the uth and the tank to be problematic as it causes a gap in contact of the uth and the bottom of the tank. Those people have found placing the probe under the uth to work better to provide a more uniform heat pattern. So doing it this way it would be tstat probe, uth, then the tank bottom. You can still use the same items to secure it.
Note that when you secure the tstat probe you will get best results by taping the wire behind the probe to secure it. You want to avoid covering the probe itself as it can get insulated and cause inaccurate readings to the tstat which will give you a hotspot that is not in the desired temp range.
Tape on snake is really bad as it can tear their skin from their body. Use Google images to see some pics of what tape can do. You can also search the forum as I know I have seen pics here as well.