A local licensing board: may not renew a license if the board determines that the license holder is not qualified to obtain a license renewal; but shall issue to the license holder by way of renewal the class or type of license for which the board determines the license holder is qualified. Subject to paragraph (2) of this subsection, a local licensing board shall deny a license renewal application if during the license year the license holder was convicted of a State or federal offense that, in the judgment of the board, renders the license holder unfit or unqualified to obtain a renewed license. A local licensing board: shall hold a public hearing before renewing a license under the circumstances described in paragraph (1) of this subsection; and may inquire into all relevant facts and circumstances concerning the offense at the hearing.