Question: How much damage would a space probe cause if it can get about 4 lightyears away in 10 years and doesn't have any brakes when it arrives? Could it cause a global extinction event on the planet it was sent to? Do actual concept probes think about this?

Answer: 
Calculating the damage done due to an impact is an imprecise business, but we could use the [KT extinction event](https://en.wikipedia.org/wiki/Cretaceous%E2%80%93Paleogene_extinction_event) (that finished off the dinosaurs) as a benchmark. This impact had [an energy of around $4.2\times 10^{23}$ joules](https://en.wikipedia.org/wiki/Chicxulub_crater#Impact_specifics). The question is then how fast our probe would have to be going to deliver this much energy.

For a relativistic projectile the total energy is given by:

$$ E^2 = \frac{m^2v^2c^2}{1 - v^2/c^2} + m^2c^4 $$

and the kinetic energy is just this energy minus the rest mass energy $mc^2$.

Let's assume our probe has a mass of a ton ($10^3$ kg), which is around the mass of the [Voyager probes](https://en.wikipedia.org/wiki/Voyager_program). In that case to match the energy of the Chicxulub impact would need a speed of around $0.99999998c$. You're suggesting a speed of $0.4c$, and at that speed the kinetic energy would be around $8\times 10^{18}$ joules, which is a factor 50000 lower than the Chicxulub impact energy. Even so I wouldn't like to be standing underneath it when it hit.

But there are a couple of points that need to be made.

Firstly space is big - really big - and it's mostly empty. The chance of a probe hitting anything is so ridiculously small that no-one is going to take it seriously.

Secondly NASA does care what happens to its probes and this is part of the mission planning. For example [the Cassini probe is going to be deliberately crashed into Saturn](https://en.wikipedia.org/wiki/Cassini%E2%80%93Huygens#Spacecraft_disposal) where the heat of reentry will destroy it (and any Earth life forms that might be hiding on it).
First of all, even without an artificial braking system, a spaceship can slow down using tidal forces of the planets/astronomical bodies it passes by, just as it can speed up using gravitational assist. So, it will not necessarily reach cataclysmic speeds simply by travelling for a long time through space.

Now, let's estimate the energy that will be released if the space probe *[New Horizons](https://en.wikipedia.org/wiki/New_Horizons)* crashed into a planet like earth. *New Horizon* has a gross weight of about 400 kg. Its last recorded speed (the world record currently) is 16.26 km/s = 16260 m/s. Let's assume it crashes with this speed. And all of its kinetic energy is converted into heat. The heat released will be about 53,000,000,000 J. A ton of TNT produces about 4.184 $\*$ $10^9$ J of energy. The energy released in the crash event is about 10 times this energy. That's about enough to blow a large enough tunnel in an average mountain. The planet won't even notice.