Chris Brown -- L.A. Prosecutor Keeping Close Eye on Miami Robbery Case

Chris Brown is being watched ... watched closely by the D.A. who prosecuted him for beating Rihanna ... because the latest incident in Miami could trigger a full court press in L.A. to send Brown to prison.

Sources tell us ... the L.A. District Attorney's Office is well aware of the robbery-by-snatching investigation of Brown in Florida ... and they're waiting for the L.A. County Probation Dept. to recommend what action, if any, should be taken.

In case you forgot ... and how could you forget? ... Brown was sentenced to 5 years probation for beating Rihanna in 2009 ... and one of the terms is that he obey all laws.

If officials determine the allegations against Brown are true -- that he "snatched" a cell phone from a woman in Florida -- his probation could be revoked and he could be thrown in prison for 4 years.