Jocelyn's answer is very good.
Here's my answer:
Perhaps means maybe.
Maybe means perhaps.
How do you like my answer so far? :)
Maybe and perhaps are synonyms.
Both mean that there is a chance (something is possible / could happen / might happen).
'Probably' means that there is a high or low chance that something will happen or will be true or ... Probabilities can be calculated mathematically.
For example - What is the probability that A, B or C will happen?
Probability of A happening = 10% (0.10)
Probability of B happening = 11% (0.11)
Probability of C happening = 79% (0.79)
So we can say that C has the highest probability of happening.
In English, when we talk about tomorrow's weather we talk about the probability of precipitation (rain or snow) (POP/PoP). It is usually expressed (written or spoken) (expressed means described) in mathematical terms, e.g. There is an X% probability (or chance) that it will rain tomorrow.
I can't believe it - I actually remembered something from all those math classes I took many years ago :)