They use the number of stars in the observable universe instead of the number of stars in the whole universe. This ruins their calculation. I wrote a little more here
We can take it as a calculation for 'number of technological civilizations in our past light cone', whose messages we could receive.
But the lower bound of this is still well below one. We can't use our existence in the light cone to infer there's at least about one per light cone. There can be arbitrarily many empty light cones.
A paper published in Astrobiology: A New Empirical Constraint on the Prevalence of Technological Species in the Universe (PDF), A. Frank and W.T. Sullivan.
From the abstract:
They say we now know with reasonable certainty the total number of stars ever to exist (in the observable universe), and the average number of planets in the habitable zone. But we still don't know the probabilities of life, intelligence, and technology arising. They call this cumulative unknown factor fbt.
Their result: for technological civilization to arise no more than once, with probability 0.01, in the lifetime of the observable universe, fbt should be no greater than ~ 2.5 x 10-24.
Discussion
It's convenient that they calculate the chance technological civilization ever arose, rather than the chance one exists now. This is just the number we need to estimate the likelihood of a Great Filter.
They state their result as "[if we set fbt ≤ 2.5 x 10-24, then] at in a statistical sense were we to rerun the history of the Universe 100 times, only once would a lone technological species occur". But I don't know what rerunning the Universe means. I also can't formulate this as saying "if we hadn't already observed the Universe to be apparently empty of life, we would expect it to contain or to have once contained life with a probability of 1024", because that would ignore the chance that another civilization (if it counterfactually existed) would have affected or prevented the rise of life on Earth. Can someone help reformulate this?
I don't know if their modern values for star and planet formation have been used in previous discussions of the Fermi paradox or the Great Filter. (The papers they cite for their values date from 2012, 2013 and 2015.) I also don't know if these values should be trusted, or what concrete values had been used previously. People on top of the Great Filter discussion probably already updated when the astronomical data came in.