We have studied the effects of interactions between particles on the dynamics in a colloidal dispersion system using the time-dependent density functional theory. We consider a hard-sphere probe particle fixed at the origin and hard-sphere colloidal particles suspended in a solvent that flows at a constant velocity against the probe particle. We calculated the density fields of colloidal particles, forces acting on the probe particle, and friction coefficients for small volume fractions of colloidal particles. The results show that hard-sphere interactions between colloidal particles decrease the forces and friction coefficients. The effect of the interactions is more significant for small colloidal particles than for large particles. The effect also becomes weak with increasing velocity of the solvent.