Well straight off the bat I'd say that "disclose" is the most different of the three words, "expose" and "reveal" can be used synonymously in some contexts. When information is being "disclosed" people are expecting to hear it.
E.g. Full details of the incident will be disclosed on Friday. (Now everyone is waiting to hear the disclosure.)
"Expose" and "reveal" however, are used when private or unexpected information comes to the public's or somebody's attention.
E.g. News reporter: Tonight, we can reveal the gross misuse of public funds by government officials.
E.g. News reporter: Tonight, we expose the true cause of the financial crisis.
In both examples the information is unexpected/shocking/damaging.
"Expose" and "reveal" have a lot of other uses as well, but I think this was the usage you were enquiring about. Hope it helps!