The probability or likelihood of something happening isn't just with the "might" or "might not" statement, but in the surrounding context. The speaker thinks the listener has a particular assumption and wishes to contradict it.
It might not rain.
When I say this it implies that I think we both understand there is a strong chance of rain. I haven't said very much yet about the new probability of rain. It may be a hope, or I may have new information.
On the other hand, if we'd both been aware of only predictions for good weather, it's hard to think it would make sense for me to say "It might not rain." You'd ask me if I was talking about the weather somewhere else or if I knew something you didn't. But "It might rain" would make sense, even just as a caution to bring an umbrella.
Take another example:
I might be home by 7:00.
If you require an exact answer from me, much as with "I might be coming," you'll have to wait, or insist that I be more specific. I'm not giving you very much information about my certainty with this one statement. But my statement again doesn't occur in a vacuum. My statement implies that the listener and I have an expectation about when I'll arrive home. If I was trying to arrive at 7 or at 8, that can change the meaning from something like "Don't count on me getting there on time" to "I could be early".
As Robusto pointed out (thanks!), the tone of voice can make a difference as well. For example, the listener and I could both have the same understanding - that I am trying to arrive by 7 - but I can say the same phrase and mean different things:
If I say "I might be home by 7:00" I could either be encouraging the listener to hope or, with a certain amount of doubt in the tone of voice, express the opposite.
So when as a speaker, I say
I might be coming
I might not be coming
it almost says more about what I think you, the listener, assume, than about what I (speaker) am actually going to do. I'm still unsure about what's going to happen, but I don't want you to get the wrong idea. I'll tell you "No, no, I might be coming" so you don't get the idea I've already decided not to go; I'll tell you "Actually, I might not be coming" so you don't think I've already committed and count on me to bring all the drinks.