Arduino detects voltage on ground
Yes, @SHG is right, and you confirmed  my suspicions.

The analog input measures the voltage difference between the arduino ground and some point above arduino ground.

You can only measure relative to the Arduino's ground, not measure some other point in another circuit.

You have to connect the ground of the Arduino to the ground of the remote circuit in order to get any form of meaningful signal.  In your case you would basically be measuring the Arduino ground since they would both be connected together.