BD700 Captain reported the loss of the #1 Air Data Computer caused unreliable air data and resulted in an air turnback and precautionary landing at departure airport.

Narrative

During the initial climb from ZZZ to ZZZ1 we experienced a sequence of erratic events starting from landing gear unsafe to wind shear advisory; immediately followed [by] unreliable airspeed and altitude from all our ADC (Air Data Computer) systems. It became immediately clear that [the] ADC was most likely the issue. We immediately advised the Control Tower and we were asked to contact ZZZ2 Center. We advised ZZZ2 Center of the situation we were experiencing and told them that we couldn't maintain a reliable airspeed and altitude; we advised them of our intention to return back to ZZZ Airport Runway XXL.Once we were vectored to left downwind leg; upon reaching what we believed was 8;000 ft.; we had the caution message ADC1 MIS COMP. We followed the QRH checklist but we still couldn't determine the proper altitude and speed. We both agreed that the right-side PFD had more reliable information compared to the left one so I decided transfer control to the pilot on the right seat. We also agreed that [it] wasn't necessary to [request priority handling]; [due to] having positive control of the aircraft; being in VMC conditions; and in the traffic pattern with the assigned runway in sight. Once ZZZ2 Center handed us off to ZZZ Control Tower the right seat pilot landed the plane safely to Runway XXL. We immediately advised [the] Maintenance Department and wrote a discrepancy report.The possible causes that we are considering are either moisture or part of the deicing fluid or the combination of both that were trapped inside the pitot tubes lines feeding wrong information to the Air Data Computer.