Most complex contingent events, and even many simple ones, would be
considered extremely improbable if they could be viewed prospectively.
Generally, however, they are viewed only retrospectively, when
probability is no longer germane.
Like most people, you likely have experienced the "it's a small world"
phenomenon several times in your life. I.e., two people from the same
neighborhood or school, perhaps even old friends, happen to meet each
in a huge city far from home. "What are the odds ...?!" they might
say. But such events, considered cumulatively, are not especially
rare.
Back in the 1950s, RAND Corporation published a book entitled, "A
Million Random Digits," for use in mathematics and statistics
projects. Although it was produced with the best random number
technology available at the time, and *as a whole* doesn't appear to
have a discernible pattern, there are plenty of small-scale patterns
within the overall sequence. E.g., you might see something like
"0101010101" that in isolation would appear quite improbable.
How difficult do you think it would be for one person to win 12
straight coin tosses of a fair coin? Would that be a "normal" sort of
event, or a freakish, mysterious occurrence that would have to
indicate either ESP or a "fix"? Well, all you need to do to identify a
person who can win 12 straight coin tosses is to go to a medium-size
rock concert. Hold a 12-round coin flip tournament with the audience
members (you need only 4,096), and the champion will be a person who's
just won 12 coin tosses in a row. (You'll also have multiple people
who won 11 straight tosses, and 10 straight, etc.)