I postulate that our brains have a shock-detector. The shock value of a sure thing is zero, so it doesn't even register. The shock value of an impossible thing is infinite. To accommodate a wide range of shocks, the response of the shock detector is logarithmic. So for an event of probability \(p\) we register the shock value of \(sh = log (1/p)\).
The way this fails to match up with intuitive meaning of boredom is that it claims that white noise is the least boring thing possible.