Hot to ground voltages on an ungrounded 3 prong outlet
Your GFCI Tester tells it all. The ground conductor needs to be connected at the device and all the way back to the panel ground. Otherwise it is just a loose wire and the readings you are getting off of it is a "ghost" reading or a voltage reading of a very low amperage output. So it just means it is not connected properly.

The NEC Is specific about changing out a 2 prong outlet to a three prong. You must install a GFCI outlet instead, or install a GFCI device and feed the entire circuit through it, and all receptacles then must be labeled as ungrounded. If you purchase a GFCI receptacle these labels will come with it. 

I did an edit on this answer to install two examples of what I am talking about which might help you understand.

 



Just remember your installation does not have a ground.

Stay safe and good luck.