The Kentucky Constitution states,
All men are, by nature, free and equal, and have certain inherent and inalienable rights, among which may be reckoned: ...
Seventh: The right to bear arms in defense of themselves and of the State, subject to the power of the General Assembly to enact laws to prevent persons from carrying concealed weapons.
Kentucky courts have rightly read this as protecting people's rights to have guns for their own self-defense ("in defense of themselves") and not just for the common defense. Does this, though, apply to convicted felons? Last Thursday's Kentucky Supreme Court decision in Posey v. State answers "no," but in much more detail than all the other state court decisions that have likewise held that felons are implicitly excluded from state constitutional rights to bear arms. There's even one dissenter, who would hold that some felons (though probably not those convicted of the more serious felonies) do have a right to bear arms under the Kentucky Constitution. If you're interested in either the right to bear arms or the broader question of how courts should interpret Bill of Rights provisions, these opinions are much worth reading.