Pilot reported a smoke warning indication illuminated during climb. The flight crew returned to the departure airport where post flight it was found a smoke sensor had an electrical short.

Narrative

Appx 20 minutes after take-off from ZZZ; at 17;000 ft. MSL; red 'SMOKE AVIONICS BAY' EICAS message illuminated along with corresponding master warning light. Crew performed memory items in accordance with Checklist; requested an immediate return to ZZZ (closest suitable landing airport with fire rescue). While enroute back to airport crew continued with the applicable SMOKE AVIONICS BAY checklist until they had to switch to the descent checklist and prepare for landing Runway XX at ZZZ.Crew requested Crash Rescue to be on seen in case of fire. At this time SMOKE AVIONICS BAY warning light had begun to go off and then back on multiple times; but crew could not detect any smoke or fumes in the aircraft. Airplane was landed without incident and crew elected to shut airplane down on the ramp without starting the APU to avoid introducing any other possible flame or smoke sources. The apparent cause of the incident was the sink in the lavatory was trickling water; it overflowed and the water made its way into the avionics bay under the airplane; causing an electrical short with a smoke sensor. The crew was not aware that the water was on during the start; taxi and departure sequence of the flight. After discussing the situation with other crew members and Maintenance it was suggested that we turn water supply off to the sink itself since it is never really used. (hand cleaner is used instead).