* Inertia: The space probe, like all objects, has inertia. Inertia is the tendency of an object to resist changes in its motion. This means that an object at rest wants to stay at rest, and an object in motion wants to stay in motion at a constant speed and direction.
* Rocket's Push: The rocket's engines provide a force that accelerates the space probe. This force changes the probe's velocity (speed and direction).
* Outer Space: Outer space is mostly a vacuum, meaning there's very little air resistance. Air resistance on Earth would slow the probe down, but in space, there's very little to impede its motion.
* Newton's First Law: Newton's First Law of Motion states that an object at rest will stay at rest, and an object in motion will stay in motion at a constant velocity, unless acted upon by a net external force. Once the rocket stops pushing, there's no significant force acting on the space probe to slow it down.
In short: The space probe keeps moving because of inertia and the lack of significant forces acting upon it in the near-vacuum of space. It will continue to move in a straight line at a constant speed until something else acts on it (like gravity from a planet or a maneuver by the probe's own engines).