One would certainly expect to see a pretty massive 60Hz hum if you touch the probe tip with a finger (ground clip not connected to anything.)
Please set your scope up as shown in the screenshot below and post the image. Note that both the switch on the Probe, and the channel setting, are set to 10x, and the channel V/div is set to 10V/div and the input coupling is set to DC. Probe ground clip not connected to anything, touch tip of probe with finger. Horizontal timebase at 5 ms/div. (Your amplitude will probably be different but you should still see a clear mains hum.)