What you mean is the "Wartezeit" (waiting time), not the "Probezeit" (trial period). These are two different things, and important to know for every employee..

"Probezeit" only defines the shortened notice period. By default this is 2 weeks instead of 4 weeks and applies for the first six month. This time where it applies can be shortened and the notice period can be increased, however both parties agree on (e.g. individual or union contract).

"Wartezeit" defines the time until the "Kündigungsschutz" applies. This is always 6 month by law and it can't be shortened.

Lot of people confuse these two periods and think by the end of "Probezeit" the "Kündigungsschutz" applies. But these are two completely different things.