There are two explanations for a safety probe depending on whether or not a universe allows ACS.
For a non ACS universe, a probe is timed to arrive at a planet in front of an attacking fleet so that a ninja attempt may be detected. A tradeoff exists between sending the probe late enough to detect a defending fleet's arrival and allowing enough time for an attacking fleet to be recalled.
ACS universes allow probes to be joined onto attack fleets using the alliance combat system, slowing your fleet and allowing time to send another probe on its own in an espionage mission to the planet. If an ACS defend fleet has been sent, this probe will show the fleet in orbit. If a fleet has been slowed with ACS probes there will be enough time for it to be recalled.
Example in ACS universe Edit
An attack lands at 23:00 server time. A safety probe is sent to arrive at 23:01 server time. The attacking fleet can be slowed by adding a probe to delay the time to 23:10 server time. Now any ACS defend (which will add ships to the safety ESP report) will show up and allow the time to recall.