Some people equate complexity with randomness/disorder because of algorithmic information is also called complexity.
Small probabilities tend to represent a highly select, unusual chain of contingencies. In the bean machine, the lefts vs. rights taken by the beans will have a more ordered structure at the tail ends. This low algorithmic information in tail-end result represents a path whose description has low algorithmic information.
How many things must go just right (or just wrong) to get the unusual result? It is highly contingent. Maybe specified contingency is a better phrase?