When considering the probability of Earthlike planets and life elsewhere in the universe, most probabilistic estimates (for example, the famous Drake equation) tend only to focus on alien civilisations we might potentially be able to contact.
Working outside our light cone and assuming that our civilisation will survive indefinitely into the future provides much more opportunity, of course. The universe is likely to last a very very long time, and even ~13 billion years in we're still only a small fraction into the universe's projected lifespan.
The longer we look and the more data we gather about the universe around us, the more it's becoming clear that we're not really very special - just another rocky planet amongst an almost uncountable number of others just like it. Even with the smallest odds of life arising on an Earthlike planet, life may be very common after all.
According to a new theoretical study, when our solar system was born 4.6 billion years ago only eight percent of the potentially habitable planets that will ever form in the universe existed. And, the party won't be over when the sun burns out in another 6 billion years. The bulk of those planets - 92 percent - have yet to be born. Based on the survey, scientists predict that there should be 1 billion Earth-sized worlds in the Milky Way galaxy at present, a good portion of them presumed to be rocky. That estimate skyrockets when you include the other 100 billion galaxies in the observable universe. This leaves plenty of opportunity for untold more Earth-sized planets in the habitable zone to arise in the future. The last star isn't expected to burn out until 100 trillion years from now.