The probe was not part of the CM's forward hatch, but a fully separate part that was left in the LM and discarded once the mission was complete. When not latched in place in the CM, the forward hatch was stowed the left-hand equipment bay, next to some key elements of the environmental control subsystem.
The following information comes from Section 2.13 of the Apollo Operations Handbook.
Shortly after translunar injection, the spacecraft transposition and docking phase takes place ... When the probe engages the drogue with the use of the capture latches, the probe retract system is activated to pull the LM and CSM together.
Upon retraction, the LM tunnel ring will activate the 12 automatic docking ring latches on the CM and effect a pressure seal ... The CM forward hatch is removed and the actuation of all 12 latches is verified. Any latches not automatically actuated will be cocked and latched manually by the crewman.
At the same time, the LM electrical umbilicals are connected and so on. Notably, during this operation, the probe-and-drogue is still in place between the two vehicles -- the tunnel is blocked.
Once in lunar orbit, the tunnel is repressurized. The probe assembly and drogue assembly are removed from the tunnel and stowed in the CM... After two crewmen transfer to the LM, the CM crewman retrieves the drogue from its stowage location in the CM, passes it through the tunnel, and helps to install and lock it in the tunnel... The probe assembly is then retrieved from its stowage location in the CM and installed and preloaded to take all the load between the modules.
The probe and drogue then are used during the undocking sequence, and again when the LM comes back up from the surface, to pull the LM into docking position. Then the whole tunnel-clearing process is repeated, with a notable change:
After rendezvous and docking in lunar orbit... the LM crew opens the LM hatch while the CM pilot removes the tunnel hatch. The drogue and probe are removed and stowed in the LM.
At that point the astronauts and everything they want to take home get pushed through the tunnel and stowed in the CM. Then --
equipment in the CM that is no longer needed is put into the LM, and the LM hatch is closed
When the LM is finally cut free (this time using a ring of detonation cord rather than a mechanical system), the probe-and-drogue equipment is left inside it in an unstable lunar orbit, to eventually crash into the moon's surface, along with all the other gear they wouldn't need for the trip home.