Rare-gas clusters produced in a supersonic expansion into vacuum are doped with alkali-metal atoms using the pickup technique. We give here a detailed description of our experimental apparatus, which is suitable for electronic spectroscopy of any desired gas clusters doped with low-temperature melting metals. Potassium-doped Ar clusters (average size N approximate to 2000) are investigated by beam-depletion (BD) spectroscopy as well as laser-induced fluorescence (LIF) spectroscopy. The observed BD spectra are strong and exhibit several broad peaks within the scan range of the Ti:sapphire excitation laser; only one weak band is observed instead in LIF spectra. This situation resembles the one previously observed for K-doped H-2 clusters [Callegari et al., J. Phys. Chem. A 1998, 102, 4952] where it was argued that fluorescence is either quenched or strongly red-shifted by the cluster. We investigate BD spectra as a function of the potassium vapor pressure in the pickup cell, and we perform an extensive analysis of the pickup process, necessary to separate the overlapping spectral contributions of different species. We tentatively assign parts of the spectra to the monomer, singlet dimer, and doublet trimer, of potassium residing on the surface of the cluster. To support our trimer assignment, we perform complete active space self-consistent field (CASSCF) calculations to determine the lowest 12 electronic spin-doublet states of free K-3. We find several candidate transitions in the region of interest. Although a definite assignment is not possible because the energy shifts due to the perturbation by the Ar cluster are not known, our theoretical and experimental data compare favorably with existing spectra, and with simulations, of the closely related Na-3-molecule, upon suitable scaling of its energy-level structure.