It's probably voltage induced from the nearby wires. Some meters have a low impedance mode for these exact occasions, it makes the input impedance of the meter just low enough (about 2k, IIRC) to put a bit of load on the measured nodes, so the ghost voltages disappear.
I can't say I would advise you to attach a resistor between the wires and try remeasuring. You wouldn't want things to blow up in your face, should you make a mistake.