Zener voltage clamping

[tester43]

Hi again,

So ... here I am adding zener diode 1n4728 as overvoltage protection.
Voltage is AC rectified unfiltered.
To my terrror and shock I found that near zero zener stops at very special value around 0,7-0,8V. I was expecting 0.
Looks like typical p-n diode voltage.
It's very typical circuit: AC transformer output + load (8ohm).
From one end of load goes 680ohm resistor + zener and to GND on rectifier.
Probe is between resistor 680 and zener.
High end is as expected around 3V.
But why low is not ground?
Is it because of minimal required current?

But here is my "poor man scope" picture attached.

[tester43]

I will reply to myself because I am stupid.
Once voltage drops below 3,3 it's not this diode any more.
It's coming form totally different place.
Please feel free to ignore my message.