In the US there often is a formal probationary period at larger companies which mainly accomplishes one thing: reduce the HR red tape if a new hire isn't working out. During the probationary period it's generally easier to make a case (i.e. little or no documentation needed) that 'they're not working out' and HR will be OK with it vs. after the probationary period, you typically have to 'document' them out of the company.
I'm in the USA, and this (probationary period) has been the case with every job I've had in the past 30 years. I've never heard of a company not doing this in fact.
Same here. Though many mid-size / smaller companies might not advertise this fact (their HR policies are often a bit more ad hoc than larger companies if they haven't been involved in as many labor lawsuits)... but pretty much if there's an HR department, the probationary period exists.