Lacking both observation of ET life and a good understanding of how life originated, this question remains a great mystery. One can never completely disprove the existence of extraterrestrial life.
There are two basic approaches to potentially answer this: one theoretical and one empirical.
If a good theoretical understanding of the origin of life, abiogenesis, is achieved in laboratories, then the frequency of it happening given different observed exoplanetary conditions could be estimated.
Empirically, of course we might be lucky enough to discover some statistics of actually observed living exoplanets.
But there's a third way too, the SETI way. The evolutionary steps to intelligence, to technology, to space travel all seem to benefit the proliferation of life and thus would tend to become more common over time, if they at all occur. Considering the small size of the Milky Way compared to its age and reasonable space traveling and settling speeds, one could put upper limits on how common life is.
If anyone anytime anywhere in the Milky Way developed space travel to its nearest stars, they (their offspring) should be everywhere today! They won't need to travel further than a few light years to "seed" the entire galaxy, because their Sun does the traveling through the galaxy for them. Our Sun makes a revolution every 0.25 billion years, 18 full revolutions since it was formed. We know that dinosaurs lived on the other side of the galactic center. Traveling to the nearest stars over time spreads a space traveling civilization to all over the place. If we don't find any signs of artificiality during the next few decades, given the rapid advancements in telescopy, we can say that space traveling civilizations never happened anywhere (or got too exotic for us to discover even if under our nose). And that might be extrapolated to how frequent biological evolution is overall. And most importantly, what unique event happened here to make us walk on the Moon.
On Earth, life has settled every habitable spot on Earth (everywhere where liquid water is found, life is also found). Maybe life tends to settle on interstellar scales too?
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