Calculating probabilities is no fun. If I remember statistics class correctly (loooong time ago), for each generation back you multiply by 50%. If the ancestor actually was a blue, then it definitely gave a copy of dilute to the kit. If the ancestor was a black known for certain to be carrying dilute, then the chances it gave it to the the kit are 50/50. And after that, the chances are 50/50 for each generation.
So, great-grand blue, grand carrier, parent unknown, kit unknown = 100% x 50% x 50% = 25% chance
If the great-grand was just a carrier, then the chance goes down to 12.5%
What I can't remember is, if you cross those two together, do you add or multiply the chances? One way gives and answer of 37.5%, the other gives an answer of just 3.125% It was just too long ago, that class I had to take, but I think you're supposed to multiply. So that would be a 3% chance, pretty depressing. If everybody is carrying chocolate, that means you also have a 3% chance of lilac.
Hope that helps you plan your strategy!