The nearest star system to our solar system is the Alpha Centauri system, which is approximately 4.37 light-years away. Since the speed of light is the fastest speed in the universe, it would take light itself 4.37 years to travel that distance.
If we assume a probe could somehow travel at the speed of light (which is not currently achievable for massive objects according to our understanding of physics), the journey from Earth to the Alpha Centauri system would also take approximately 4.37 years from the perspective of the probe.
However, it's important to note that from the perspective of observers on Earth, the time dilation effects of relativity would come into play. As the probe approaches the speed of light, time dilation would cause time to pass more slowly for the probe relative to Earth. Therefore, while the probe may experience a relatively short journey, a significant amount of time would still pass on Earth.
It's worth mentioning that the scenario of traveling at the speed of light for massive objects violates our current understanding of physics and is purely hypothetical. As of now, we do not possess the technology or means to achieve such speeds for objects with mass.