We attach a lot of meaning to coincidences. On the one hand, we see them as significant; on the other hand, you have the TV show detective pronouncing that he doesn't believe in coincidences.
The first thing to understand is that everything is a coincidence.
All a coincidence is, is two events happening at the same time. In that sense, everything is a coincidence because whenever one event is happening, a near infinitude of other events are happening at the same time.
What we CALL "a coincidence" is two events happening at the same time TO WHICH WE ATTACH SOME MEANING OR SIGNIFICANCE.
Some meaningless coincidences exist against astronomical odds. Let me think back to two events I can correlate in my mind. Here's one. I remember getting home from a movie, turning on the TV, and learning that Princess Di had been killed in a traffic accident. Clearly, it happened while I was watching the movie.
Now, what are the odds against Princess Di dying while I was watching a movie? They are so great that the odds against that correlations must be in the billions if not trillions to 1. Yet, that isn't an interesting coincidence. Coincidences with much better odds turn out to be more interesting, such as running into an old girlfriend who was back in town for a visit in the movie theater lobby.
Think about coincidence and you'll see it's a concept you probably should have thought about before.
Once you understand the nature of coincidence, you can catch people misusing the concept all the time. For example, theists will use the existence of humankind and other life on Earth demonstrating the existence of God due to the astronomically high odds against it.
What I hope I've shown is that things happen all the time against astronomical odds and that this fact in a particular case really proves nothing at all.
In the case of life popping up in a universe that, so far, seems largely barren of it, one has to bear in mind that as long as it's possible for life to exist, however difficult it may be to come into existence, we now know that there are at least billions of galaxies, each with billions of stars, so that as long as life is possible at all, it's almost certain to happen somewhere at some time, even if we'll never where and when.
Here's another one. You hear something like "Researchers have discovered that eating (name the food) doubles your risk of getting little finger cancer." Now, let's assume little finger cancer is so rare that we each have a statistical risk of contracting it over a lifetime of 1/400 billion. Doubling the risk increases the chance to 1/200 billion. Either way, 1/400 billion or 1/200 billion, the risk might as well be zero for all practical purposes. I'd certainly play Russian roulette to win $1 million with 1/200 billion odds, wouldn't you?
Periodically, one reads stories about something that doubles the risk of breast cancer. Well, while most women will not get breast cancer, it is nevertheless a fairly common form of cancer and modifying one's behavior in some small way to lessen the risk certainly makes sense, but then other people will hear that there is a risk associated with, say, a vaccination of some sort and decide to forgo vaccination for their child to avoid a risk that borders on the imaginary.
** Two observers correctly disagree about supposedly coincident events
Strip "meaning" out of 'coincidence' and leave behind a neutral concept of two events occuring at the same time -- simultaneous events (B and A).
An alleged common sense view -- B occuriing simultaneously with A will be agreed upon by any two observers. In the parochial fiction known as everday reality, as Einstein noted: "Common sense is the collection of prejudices acquired by age eighteen." -- Special Relativty does away with common sense space and time, introducing spacetime:
1. The (identical) laws of physics apply in each *inertial reference frame*
2. The veocity of light [2.997*10^8 m/sec] is the same for each *inertial* observer
...an immediate consequence of these postulates (of special relativity) is that two inertial observers disagree about whether two events are simultaneous. Dray, Tevian. The geometry of special relativity. CRC Press. 2012. pp. 3,5.
A supposed counter-intuitive concept -- the relatvity of simultaneity -- actually turns out to be a "brute fact" which any future theory of physics can not ignore. Only a little algebra and a little more patience will allow anyone who is not an anti-science fundie to *demonstrate* Einstein's basic insight.
Xian ignorance about probability stands in the way of understanding why the "anthropic principle" is garbage-out. But, that's a different kind of warped common sense.
In any case, concepts so basic -- so unquestioned but really so misunderstood -- as simultaneity and probability -- their clarifications stand as intellectual achievents of the highest order brought about during the last century. They are not, and never were common sense -- to know them correctly, they must be learned with due diligence.
I was always confused when asked if I believed in coincidence...I always thought to myself, "Do I believe that 2 unrelated phenomena can occur at the same time?....duh". I suppose it's sorta the inverse of asking if you believe in fate.