If I say maybe something will happen, I say that it may or may not happen. I don't say anything about the chances of it happening, how likely it is to happen.
If I say something will probably happen, I say that chances are good that it will happen, that it is likely to happen. I am expressing an opinion about the chances of it happening.
If I say "Probably A will happen", I'm saying that maybe it will happen and it is likely.
However, if I say "Maybe A will happen", then I haven't said anything about its chances. It may not be probable that it will happen, but you can't tell from the sentence.