The Fermi paradox is the alleged inconsistency between the lack of evidence of extraterrestrial intelligence and the various high estimates for its probability. The solution to the paradox has implications for the long-term future, in particular the feasibility of interstellar colonization and the likelihood of extinction.
The expected number of interstellar civilizations observable from Earth is the product of the number of planets in the galaxy and the following three probabilities:
Since the number of planets in the galaxy is in the hundreds of billions, even very small values of the three probabilities would imply that we should see many interstellar civilizations. However, we observe none. This means that at least one of the probabilities must be extremely low.
The second probability is most concerning, since it suggests something about the future of humanity. If it is the extremely low probability, then this means either that interstellar colonization is infeasible or that humanity is extremely likely to go prematurely extinct before engaging in it.
Generally, the more highly we rate the first and third probabilities, the lower the second probability would have to be, which should decrease our credence in the possibility of humanity ever leaving the solar system.