Fundamentally either use the (special) right probe for the job, or the (special) right scope for the job,
or don't do the job.
That about sums it up perfectly
For those few 2019 Darwin Award Contenders that still won't buy:
It can be done ***IF*** the isolation transformer is a TRUE isolation transformer (most times NOT, without a hack or two, or three...)
and physically isolated from the surrounding area (rubber feet, wooden box, custom leather profilactic)
Once confirmed that you have indeed a TRUE isolation transformer, properly zapped and SAFETY pass granted with an insulation tester at 250/500v,
and good solid shake-proof internals and secured cable tied wiring,
then, and only then, do you begin to learn the correct method to use it with a scope for that 'one off job' that some will do... regardless of the advice and cautions presented by experienced (and perhaps bitten) folks here,
some that probably took out a scope or two, and luckily not an eye or two, and or a heartbeat skip or two.. finding out how 'isolation' can go south during a heated experiment
and or fading patience
repair troubleshoot.
Ground/Earth cheaters are a no no especially if the scope has a metal housing and or touchable screws or metalwork, and the condition or insulation of the scope transformer is unknown or old,
and maybe an aging capacitor or two tied to metal chassis, to keep interference levels low..
and user risk levels high
One must also confirm just what's coming out of the wall socket to begin with, and verify all power cabling to the isolation transformer and scope are in good shape and proper polarity.
The scope probe leads, clips and 10x switch and internals,
are they REALLY ok ?
or a drama about to unfold when moved about, even though everything else 'appears' perfect ?
Even if you get it all spot on perfect, I would have PPE eye-wear, thin leather gloves, long sleeves shirt and rubber sole shoes/boots,
i.e. I don't want to come into contact with anything!
This way chances are better you only pay out for fried electronics and not on hospital/funeral fees if or when it all goes horribly wrong.
I can keep going, but hopefully I've painted a fair picture of -Murphy Isolation-
If you're not 110 percent sure and or experienced, with someone nearby just in case, DON"T DO IT !
FWIW those experienced Youtubers and forum gurus posting their methods won't be there to bail you out...