For your purposes, random or not isn't relevant. As for your mental impression of reality, two points: truly random events tend to clump; the "year of the shark attacks" was media-created fiction.
Actually the way I interpreted the promo for “random or not” was conspiratorially. That is to say some clandestine group conspired to shoot cops. My second thought was that of copy-cat, e.g. one shooting inspires another. Neither of which would be truly random. But yes, I do agree, the universe is full of randomness to which we impart coincidence or purpose e.g. the flipping of a coin 1 million times might include a subset series of 50 consecutive landings on heads, and if you only looked at a grouping of 70 flips which included those 50 you might believe there was some imbalance in the design of the coin, or the flip etc...