Conrad Murray Prosecutor Next Move -- Judge

3/19/2012 5:00 AM PDT

Conrad Murray Prosecutor's Next Move -- Judge

File under "Nothing succeeds like success."

David Walgren, the L.A. County Deputy District Attorney who put away Dr. Conrad Murray ... has thrown his hat in the ring to become an  L.A. County Superior Court judge.

Walgren -- who is considered one of the best prosecutors in L.A. County -- has submitted an application to the Governor's office.

Sources connected with the process tell TMZ ... Walgren's application is being taken "very seriously."

If you place a bet that Governor Jerry Brown will send Walgren shopping for a black robe, your money is probably safe.