Upper panel: probability distribution of the suppression factor for WDs with a close (purple) and a wide (blue) substellar companion. The shaded region indicates the 1σ confidence interval. Lower panel: probability distribution of the protection rate for WDs with a close companion (purple). The green shaded region represents the protection rate from N-body simulation with a system separation of 0.01 au. The green dashed line shows the simulation result for the system SDSS J1557+0916.