Remove the probe from the side of the keg and let it sit in the air for a while and read the air temp. I'll bet it will still read very close to 40 F. Whatever the air temp is inside the fridge, that will be (or very close to) to the temperature of your keg and the beer inside it. Also realize that temperature probes can be inaccurate. The thermocouple on my HERMS consistently reads 3 degrees low (as checked with a calibration mercury thermometer).
Unless your refrigerator has a problem or is very old, it is very unlikely that it will get cold enough to freeze your beer. I had a fridge do that once, but it was from the early 60's and the thermostat went bad and it ran constantly which froze everything inside. I've also seen older fridges have a cold spot in them toward the back where the coils are that would freeze things that were set near them. If your fridge is newer than 10 years old, I'd say you are pretty safe.
If you are new to kegging, I would recommend reading through this kegging article: