My house was built in 1960. The socket shown used to be a switched outlet, with one permanently live outlet and one controlled by a wall switch. I had ceiling lights installed about 15 years ago and, as part of that work, the contractor converted the socket so that both outlets were permanently live. I wanted to convert the socket to a GFCI as my circuit test showed that there is actually no ground connection. There isn't a GFCI that is controlling this socket, so it seems wrong to have a three-prong socket here anyway.
There is a cable on the left and one on the right. The blacks are joined as are the whites and the red is connected to the hot side of the socket. I believe that the red and black on the left cable are actually joined at the box containing the wall switch, although I have not been able to confirm this. As connected, there is 120V between the red and white, 120V between black and white, and 0V between red and black.
(I added the Wago connector as there was a nick in the red wire insulation)
There is 120V between the two black wires, 120 volts between the white and black on the right, and 0V between the black and red on the left. I totally forgot to measure the voltage between the black and white on the left! With the socket not wired up, the ceiling lights do not work even when the breaker is energized.
Can anyone explain how this wiring works and whether it would be possible to convert the socket to a GFCI. I can do some continuity testing on the wiring between the socket and wall switch if needed.