OK, so you connect probe tip to probe ground and get a straight line, that is good.
You then connect tip and ground to AC neutral and get the horrible mess in the picture.
What I think is happening is that the chassis if the scope is earthed via its mainslead, you are then making a connection to AC neutral with the probe earth and a large current is flowing from the neutral, through the probe cable, through the scope chassis, and out through the scope mains lead to earth.
This is a bad thing to do!
Although AC neutral is connected to earth somewhere, that does not mean that the neutral connection at your wall outlet will be at ground potential, there is often a few volts there.
If you must make measurements on this thing which is referenced to AC neutral, there are several things you can do:
Use an isolating transformer so that the DUT is floating and not tied to AC neutral.
Use the two channels of the scope in a differential mode (add + invert), put one probe on the neutral, one probe on the DUT and see the true measurment.
Lift the earth connection from the scope, to let the scope chassis "float".
I DO NOT recommend this method, although there are those around here who do. (Nigel?
)
JimB