using oscilloscope

I don't understand why they didn't connect the ground clip on one terminal of the diac and the probe on the other. I have attached the circuit and the ground clip is attached to bottom left of circuit to one of the main lines.

I can't tell from your picture but the ground lead on your scope is connected through the power cord to EARTH ground. Neither terminal of the diac would like that.

A suitable way to look at things would be to use 2 channels in the AminusB mode. That way the scope measures the difference between the probes but neither is hard connected to ground.

Why did they connect ground clip to main line, I know they are using an isolation transformer

THe GND of the probe should be connected to the B point, the common pin of two caps.

The whole circuit as this.

Also you should check that how much voltage your probe of scope could support.