Captain reported failing to ensure a new pilot had completed a pre-departure walk around correctly. The primary and standby pitot probe covers had not been removed; resulting in a rejected takeoff for an airspeed split.

Narrative

We were to reposition from ZZZ to ZZZZ. I had flown 5 legs with this SIC (Second in Command) over the preceding three days. I performed a walk around with him prior to our first leg; to judge his level of knowledge of the aircraft. Having been typed on this aircraft and flown with another Captain prior to our pairing together; he knew the exterior well. On this day; the SIC was left to preflight the exterior while I coordinated with company; loaded the FMS; and performed First Flight checks. As time of departure approached; I asked if the preflight was done; chocks removed; and cones/carpets removed from about the aircraft. The SIC confirmed that all was complete and cleared from the aircraft for taxi. We finished all checklists; started; taxied out to Runway XXL for takeoff. During the takeoff roll; thrust was set; call outs were made for Thrust set; Airspeed Alive; 80 kts. Cross checked. I looked at my airspeed to verify we had accelerated through 80 kts. My airspeed indicated 40 kts; The bottom; and starting point; of this aircraft's airspeed indication. Just as trained; I applied maximum brakes; retarded thrust; applied maximum thrust reversers; alerted Tower of our rejected takeoff; and cleared the runway. After parking back at the FBO; it was discovered that the SIC had failed to remove both the Standby and Primary pitot tube covers during his walk around. I had failed to do a final walk around after him. I discussed with my SIC the importance of a thorough and detailed preflight; and the potential consequences of anything less. I notified my Company Operations; Chief Pilot and Maintenance of the occurrence. In this case; following up on the actions and responsibilities of my SIC could have prevented this. Had I stepped out of the aircraft prior to door closure; I might have seen the covers. Always follow behind each other. Verify each others work. Never let your guard down. Ask detailed questions like; 'Are you sure?; Did you count the number of covers?' even if they sound diminutive.