Evolution is all about processes that almost never happen. Every birth in every lineage is a potential speciation event, but speciation almost never happens, not once in a million births. Mutation in DNA almost never happens - not once in a trillion copyings - but evolution depends on it. Take the set of infrequent accidents - things that almost never happen - and sort them into the happy accidents, the neutral accidents, and the fatal accidents; amplify the effects of the happy accidents - which happens automatically when you have replication and competition - and you get evolution.