We present our experimental investigations of nonlinear ground-state pump-probe spectroscopy in ultracold rubidium 85 produced in a magneto-optical trap (MOT). Nonlinear ground-state pump-probe spectroscopy is a two-photon analog of traditional two-level pump-probe spectroscopy. When a two-level atom is driven with an intense, single frequency near-resonant laser field the absorption spectrum of a weak probe field exhibits absorption and gain features not seen without the pump field. These saturated absorption line shapes, obtained under different pump field conditions, are known as the Mollow spectra. Nonlinear ground-state pump-probe spectroscopy is a three-level process, in which an intense two-photon pump field drives transitions between two components of the ground state coupled through an intermediate excited state. When the frequencies of the pump fields are tuned far from the intermediate state resonance, spontaneous emission is significantly reduced and narrow spectral lines are possible. The absorption/gain spectrum of a weak probe field, tuned in the vicinity of the intermediate state virtual level, resembles the Mollow spectrum except that new interference processes arise due to competition between two-photon pathways involving the probe field and each of the two pump fields. This interference significantly affects the probe absorption spectrum, and new features appear that are not present in the two-level case. We describe our measurements of this process, including the MOT that produces the ultracold collection of atoms, and the system of injection-locked extended cavity diode lasers that produce the phase-coherent laser fields used in our measurements.