Does the plug look like a metal cylinder, with a plastic tip and a hole in the end?
If so, one connector is the outer metal cylinder, the other is another metal cylinder inside the hole. So, one probe to the outer, the other probe pushed inside the hole. If the hole is too narrow for your probe, then you'll have to push a piece of wire inside to touch the inner conductor and touch the probe to that.
If it doesn't look like that, describe it to me (I have never used a SNES)
Breaks in the wire are common, usually just where the wire exits the power adapter or enters the plug at the end of the wire.