If you've bred the same two rabbits, chances are pretty good you'll get another; however, genetic prediction is purely statistical so theoretically you *could* get an entire litter of ermines, or you *could* get none at all.

The coloration is relatively rare mostly because people in the US don't breed for that color, though they are accepted in Europe. At the moment, I don't think it is a recognized variety in any ARBA breed, but breeders are working on getting the Czech Frosty, a breed with ermine coloration, recognized by the ARBA. Also I know at least one angora breeder who is working on ermines in hopes of getting them recognized. But since ermine is the result of recessive genes, once you start breeding ermines, especially to each other, you'll get more and more of them. Depending on what other genes your breeding stock has at the C locus, the chinchilla <cchd> can lurk behind full color <C>, or dominate/partially dominate the others (sable <cchl<, himi <ch> and REW <c>). (Incidentally, the C locus is a tricky one with lots of partial dominance issues so if you have chinchillas, I'd recommend against breeding them with sables, and vice versa, since it just messes up both colors. The other C-series genes can coexist fairly well.)
What colors are the parents, and do you have pedigrees for them? Depending on the breed, I'm guessing that in addition to blacks and chestnuts/coppers, you'll find chinchillas, blues and fawns/reds/torts in the background, although those genes can "hide" for a long time so may not show up on a 3-generation pedigree.