There is no way in hell I'd ever sign up for that. To be expected to quit your current job on the hope that the probationary period works out is insane.
Yes, I've learned that the hard way. Provided they give you payment in lieu of notice, they don't need much of a reason to let you go.
Myself and a co-worker were once let go for "performance reasons" at 10 months - just after project completion (successful). It was beyond my probationary period, and no issues where raised in the 2 performance reviews.
Their notice period was just 1 month. We were effectively cheap contractors.
My advice now is to treat offers with a low notice period (of them telling you) as a red flag. The norm is 3 months, after probation.
It's rare that people fail probation; so long as you apply for work you are actually capable of doing...