We propose an interferometer composing of a scanning tunneling microscope (STM),double quantum dots (DQDs),and a semiconductor nanowire carrying Majorana bound states (MBSs) at its ends induced by the proximity effect of an s-wave superconductor,to probe the existence of the MBSs in the dots.Our results show that when the energy levels of DQDs are aligned to the energy of MBSs,the zero-energy spectral functions of DQDs are always equal to 1/2,which indicates the formation of the MBSs in the DQDs and is also responsible for the zero-bias conductance peak.Our findings suggest that the spectral functions of the DQDs may be an excellent and convenient quantity for detecting the formation and stability of the spatially separated MBSs in quantum dots.