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The study of point defects in β-Ga₂O₃ is essential to establish it as a material platform for high-power electronics. We present results from ultrafast optical-pump supercontinuum-probe spectroscopy measurements on β-Ga₂O₃. Use of a supercontinuum probe allows us to obtain the time-resolved absorption spectra of defects under non-equilibrium conditions with picosecond resolution. The defect absorption spectra shows peaks at two energies, ~2.2 eV and ~1.63 eV, and is maximum for light polarized along the crystal c-axis. The strength of the absorption associated with each peak is time-dependent; the spectral weight shifts from the lower energy peak to the higher energy peak with pump-probe delay. We are able to fit the time and polarization dependent probe absorption spectra for all probe wavelengths, at all pump-probe delays with a single set of rate equations for a three-level defect, and thus attribute the observed absorption features to Gallium vacancies. The three levels of the defect correspond to the three charge states (-1, -2, and -3) of Gallium vacancies. Finally, our results demonstrate that ultrafast supercontinuum spectroscopy is a useful tool to explore defect states and their dynamics in semiconductors.