Laws of Coincidence

I am fascinated by the events that occur at random and yet seem to follow some hidden law of coincidence. For example, in the news recently there has been a spate of railway crossing accidents (over a short period of months) at a particular railway crossing.
I started thinking of the odds of any two objects (car and train in this instance) meeting at the same point in space and time. Something like two atoms colliding at random. There must be a mathematical equation to predict this occurrence.
A more trivial example is my personal observation of when I go for a walk. The roads are empty of traffic until I go to cross the road and then the laws of coincidence kick in and inevitably the very moment I want to cross the road, a car will appear and pass in front of me at the very moment.
I started researching coincidence and found that Carl Jung, a contemprary of Sigmund Freud was also obsessed with this phenomenon and developed a theory called Synchronicity.
I personally don't subscribe to Jung's concept of Synchronicity because it delves into the realms of spiritual/mystical. I'm more of a mathematical disciple but definitely not guru.
There have been times in my life when events have seemed fortuitous and these incidents can plant the seed of thought that there is a divine hand guiding the course of my life.
In fact many people do believe that concept and again it does verge on the spiritual.

So is coincidence really random? Does it follow some mystical guiding hand or is there a mathematical algorithm to explain it?For those who are mathematically literate, you can see Wikipedia link for explanation of the formula shown.