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When the probe is already on its way and we can neglect the station's gravitational attraction, it won't need any more propulsion and will continue to move as it started.

This is due to Newton's first law: any object will stay at rest or continue its movement at constant velocity when no unbalanced forces are acting on it.

Deep space, as you describe, virtually satisfies this conditions, as any gravitational influencing bodies are so far away, their gravitational pull is negligible. Also, in a very deep space, away from stars, dust and gases clouds, there wouldn't even be much frictional force.

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