My guess is that the police search up their identification and look for the houses they live in. They tend to find information pretty quickly when it comes to suspects. As for the distance like Stephen Paddock, I'm sure some FBI agents and police close to the area of their residence go to the shooter's homes.
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"Now! Feel death, not just mocking you. Not just stalking you but inside of you. Wriggle and writhe. Feel smaller beneath my might. Seizure in the Pestilence that is my scythe. Die, all of you."
- T.J. Lane (in his Facebook poem)