Probe ships were long-range spacecraft, built by the BnL Corporation and tasked with delivering EVE units to Earth in order to scan for lifeforms. Probe ships used a laser scanning system in order to find firm, level ground on which to land. The Axiom has two docking bays for probe ships, or ARVs (Axiom Return Vehicle).
Once an EVE unit found an example of life, the ship was programmed to retrieve the unit and return it to the Axiom. WALL-E hitched a ride on one of these ships, as he had grown quite attached to this unit and couldn't resist being without it.
The ship docked in the Axiom with the help of two docking robots. After that it was fueled by FIL-R fueler bot. The unloading of EVE units is handled by robotic arms, including 077 and 229.
Concept art of the probe ship docking in the Axiom
Artwork of the probe ship in space on its way to the Axiom