If the arrest was recent
Start with the county jail
Someone who was just arrested in Kentucky is almost always in a COUNTY JAIL, not in a state prison, so KOOL will not show them.
Kentucky has 120 counties, and most county jails are run by an elected county jailer, with no single statewide jail roster.
Some jails publish an online roster (larger jurisdictions such as Louisville Metro Department of Corrections in Jefferson County, and Fayette County, Lexington), but coverage varies and many smaller jails have nothing online.
The reliable paths for a recent arrest are the county jail's online roster, VINELink, or calling the jail's booking desk.
Kentucky has 120 counties, with jails run by elected county jailers; some post an online roster and many do not, and there is no unified statewide county-jail search, so use VINELink or the county jail where the arrest happened.