Nothing is needed to keep the probe moving.
Work Step by Step
The concept of inertia tells us that an object in motion tends to stay in motion, unless acted upon by an outside force. No force is needed to keep the probe moving. This is discussed on page 25. Even without the rocket's thrust force, it would continue moving in a straight line at constant speed. So, in all of those science fiction shows where the starship engine stops working, the crew members can just kick back and relax (as long as they were headed in the correct direction to start with).