... I'm not too sure about this probation thing... what happens if for example you are hired at a new company, you quit your job at your previous company, and after 3 months probation or so the new company decides they will not keep you?

You are now stuck without a job when you previously had a stable job (which you quit to try out the new job).

In some countries the logistics behind making use of a probationary period are too cumbersome for companies to even bother implementing probation (you need to set realistic standards for the employee,you need to give continuous feedback to the employee, you need to be on hand to assist the employee should they be falling short, you need a watertight policy regarding implementation of probation).

I think a two day probation should do the trick (the prospective employee can take 2 days off from their current job, perform some tasks in the new job, and a decision can be made from how things went )