I use "probably' when I tend/want to believe what is being said.
Not sure about "perhaps" / "maybe". hmmm.... to me, maybe, just maybe, I am more likely to use "perhaps" when I voice an opinion or make a suggestion in a cautious way. e.g, Perhaps he is... , perhaps you would like to.. I am more likely to use "maybe" when I just take a guess of something (more neutral tone)? Having said that, I guess I user them interchangeably in a lot cases too. So, don't ask me....