I checked the meaning for all 3 words and it appears that: 也许 = maybe, perhaps, probably / 或许 = maybe, perhaps, probably"/ 可能 = possibly, possible, maybe, perhaps. It seems to me that 也许 and 或许 have exactly the same meaning while 可能 looks a little different. I'm not sure if each of them are supposed to have a certain situation to be used. What situation do I use each word?
see e.g.bkrs: 可能 might (happen) possible probable possibility probability maybe perhaps #170
也许 perhaps; probably; maybe #676
或许 perhaps maybe #2652
coclusion: 可能 unlike other 2 can be noun and includes ＂possible, possibility" ("literal" translation of 可能), can be used as adjective (see sample phrases with 可能的) 可能,也许 include "probably",或许 does not (lower degree of likelihood), also note frequency ranks with 可能 most frequent, much more at bkrs
或许 are slightly subjective. They sometimes imply the intention of the speaker of believing in the suggested outcome or explanation.
也许他不是故意的。Maybe it wasn't on purpose.
The above may imply the speaker's intention of believing that
It wasn't on purpose.
A similar word,
一般, implying a stronger intention, can sometimes be substituted.
一般他不是故意的。Perhaps it wasn't on purpose.
可能 is more objective and less likely to induce such implication.
保护可能已经失败了。It is possible the protection has failed.