If you are randomly shooting a rock through the solar system, "close approach of mars within 100,000 km" is 870 times as likely as "hitting mars". That brings a 'once in 100 million years (really roughly guessing based on what I know of earth's geological history)' event down to the order of 'once in a hundred thousand years', and the proper reference class of things we would be considering ourselves this lucky to see is probably more like 'close approach of a large comet to a terrestrial body' rather than singling out mars in particular. I don't know enough about distributions of comet orbital energies to consider different likelihoods of comets having parabolic orbits that bring them closer to the center of the solar system versus further away to compare the odds of things going near the different terrestrial planets with different orbits. The gravity of a planet actually slightly increases the fraction of randomly-shot-past-them objects that hit them over just sweeping out their surface area through space, but for something with a relative velocity of 55 km/s (!) that effect is tiny.

I recommend Taleb's The Black Swan. The major premise is that people tend to underestimate the likelihood of weird events. It's not that they can predict any particular weird event, it's about overall likelihood of weird events with large consequences.