Extremely small transmission change spectra due to $4f–4f$ transitions in a rare-earth ion ${\mathrm{Eu}}^{3+}$ in a crystal and in an aqueous solution were measured, to the best of our knowledge, for the first time. By multichannel double-lock-in pump-probe spectroscopy, photoluminescence (PL) and difference transmission spectra were simultaneously recorded for an ${\mathrm{Eu}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal with broadband lamp light sources for both the pump and the probe. A very weak transmission change signal hidden behind a 1–2 orders of magnitude more intense PL background signal was readily extracted. By comparing the transmission decrease due to the excited-state absorption (ESA) and the transmission increase due to the ground-state depletion it was found in the crystal that the oscillator strengths for the $f–f$ transitions to the same final states are of the same order of magnitude for both the spin-allowed transitions from ${}^{5}D_0$ in the ESA and the spin-forbidden transitions from ${}^{7}F_0$ in the ground-state absorption (GSA). In addition, crystal-field split $f–f$ transitions that have been hidden by the intense charge-transfer band in the GSA were revealed.