$3p$ shakedown spectra of laser excited potassium atoms as well as direct $3p$ photoemission of ground state potassium have been studied. These two excitation schemes lead to the same final states and thereby provide a good basis for a detailed study of the $3{p}^{5}(4s3d{)}^{1}$ configurations of singly ionized potassium and the photoemission processes leading to these configurations. The comparison of direct photoemission from the ground state and conjugate shakedown spectra from $4{p}_{1∕2}$ laser excited potassium made it possible to experimentally determine the character of final states that are only weakly excited in the direct photoemission but have a much higher relative intensity in the shakedown spectrum. Based on considerations of angular momentum and parity conservation the excitation scheme of the final states can be understood.