I'm not an expert, but I have searched on internet and what I got is:
判る - know - like you've seen something, but you don't know much about it. Like, you know japanese. You're used to it, but you don't know how to speak very well.
解る - understand - i think it doesn't need an explanation...
分かる - know - I think it's when you have a nice knowledge about it, like you know english.
But I've searched in portuguese, so it's easier to understand because we have different words for the two meanings of "know".
It would be:
判る - conhecer
解る - entender
分かる - saber