Is it possible to send probes to nearby stars?
Yes, and no. We can send probes out of our solar system as we did with Voyager I and II, and theoretically we can direct future probes toward specific exoplanets, but alas.
The distances are so great, even for the nearest exoplanets, that we will all be long dead before they ever reach there.
How’s that I say? I mean, Proxima Centauri is only 4.2 light years away! That’s very close astronomically speaking, isn’t it?
Voyager I is the fastest of the two Voyagers. It travels about 3.6 AU per year, one AU being the distance from Earth to Sun. Proxima Centauri, also known as Alpha Centauri C, is about 268,770 AU. That would take a craft traveling the speed of Voyager I about 74,658 years to reach Proxima Centauri.
So theoretically we could send a probe out there, and when it arrives it could send a signal back to Earth. That signal would take 4.2 years to reach Earth, but would be more than 74 thousand years from now. Who knows if humanity will even still be here by then or if anyone will be listening?
That’s just the nearest exoplanets. Others are much more distant than that.