There are two different portions to this. The 1st is whether or not your ex can claim the child.
If you were divorced from your ex after 1984 your divorce decree should have stated whether he or you could claim the child. (if you were divorced prior to that let me know - but if so the child is probably to old for anyone to claim!
)
If the decree doesn't state who claims the exemption then the nod generally goes to the custodial parent (there are some tests for that though!)
The 2nd is whether or not your current husband can claim the child. Your new husband would be able to claim the child IF the home he lived in was also the home of the child for more than 50% of the tax year. (this isn't a "support" test - it's a simple test of where they both lived)
If the child didn't live in the same home as your current husband for more than 50% of the year and your previous divorce gives your ex the exemption than he can claim the child.
There are several other more in depth explanations (and tests) in
IRS Publication 501
(From your explanation of your situation it certainly sounds like your current husband should get the exemption.)