I also like Urban Dictionary's other definitions and usage of probie. 
I can see the one about "one who is on probation" being applicable to its use on TV shows. But -- CRIMINY!
It's just another piece of "workplace slang". Heck, I've heard "probie" while walking around the city. There's a satellite police station located in "my" subway station, and there are usually lots of "probies" talking to other "probies" on the platform. -And there are more, I guess you could say more "colorful" terms for officers and certain procedures I've overheard from time to time.
*I don't really watch that many police procedurals on a regular basis, so I guess I don't hear the term as often as you do. As for "intubate", well, I know a couple of interns and doctors, and it is a common procedure, so... Although, "stat" being used in non-medical situations... meh...