Another response from Yahoo!:
Disbelief is shocking disagreement without understanding of the reasoning. (He was in total disbelief that she would be so rude.)
Unbelief is disagreement without shock. Can be with or without understanding; illogical (Her explaination of events was unbelievable)
Nonbelief is fully understanding and just not buying it. (His nonbelief in the subprime loan market collape resulted in his large stock market investment)
Seems like a set of choices where any of them will do as applied to a very old question.