Electromagnetically induced transparency (EIT) in K39 and K41 was probed using electro-optic frequency combs generated by applying chirped waveforms to a phase modulator. The carrier tone of the frequency comb served as the pump beam and induced the necessary optical cycling. Comb tooth spacings as narrow as 20 kHz were used to probe potassium in both buffer gas and evacuated cells at elevated temperatures. Atomic absorption features as narrow as 33(5) kHz were observed, allowing for the K39 lower-state hyperfine splitting to be optically measured with a fit uncertainty of 2 kHz. Due to the ultranarrow width of the EIT features, long-lived optical free induction decays were also observed which allowed for background-free detection.