there is continuity between scope probe ground and the neutral pin of the power cord(three pins) as shown in image.The neutral line is grounded at the source substation or transformer, but that should be just as well isolated from appliance metalwork as live.
The ground pin is the safety ground.
Can you check for continuity between the scope probe ground and power plug ground pin (without it being plugged in to a power socket)?
If there is no continuity, either the scope has a "ground isolation" jumper disconnected or the power cable / scope have have a serious problem.
If it does have continuity, the problem is either in the power outlet or the general house wiring.
Your profile says that you're in India. I would not have expected the American plug that you have shown.