This article explains the relation between the federal minimum and each state's minimum
Basically, every state must pay AT LEAST the federal minimum of $7.25, but some states set their min wage higher, such as California where the minimum wage is $8.00. If a state doesn't have a minimum wage law on the books or the state's old minimum wage is lower than the federal rate, then the federal rate applies. Some states have lower wages on the books because they simply never bothered to change their laws once the federal law went into effect in 2007. I guess they figured, Why bother? since federal law trumps state law anyway.
To answer your question, Kentucky's is $7.25.