The two outside wires are 5v (red/white) and ground(probably black/white, but I can't see in the pic). Black lead on the black/white wire, and the read lead on the red/white wire. That should read right around 5 volts.
Once you have varified that you have 5v going to the pot, you can move the red lead to the middle wire. The voltage reading there should travel between 0 and 5 volts as you turn the pot. You will have a somewhat limited travel due to the range of the pedal, so you will only see part of the 5 volt range. The main thing you are checking is that the value is changing as the pot is turned.
If the pot seems to be working, trace the middle wire to the board and make sure that you read close to the same voltage at the board. If not, the problem is somewhere between the wire and the board.
If the voltage is getting to the board fine, the pot may need to be adjusted. The pedal may not be be moving the pot far enough for the game to register a full pedal press. I think there is a test menu on Ridge Racer (not sure though, I sold mine about 5 years ago, so the details are a little fuzzy). You can look at the throttle input there to see the range in hexidecimal. You will probably need to find a manual to see what the range is supposed to be though.
If you need a new pot, I think you can get them from Happ still, but they are around $25 each. Radio Shack may have some that will work, but you may have to cut the shaft to make it fit. Probably the best bet is to put a wanted post up here and at KLOV to see if anyone will sell you a spare.
Also, it looks like it is probably fine, but I can't tell for sure in the pic, but make sure the lugs from the pots aren't touching the metal frame.