This is from 2012 but is still a great overview of Bayes's Theorem which really doesn't age.
Bayes’s theorem wasn’t actually formulated by Thomas Bayes. Instead it was developed by the French mathematician and astronomer Pierre-Simon Laplace.
Laplace believed in scientific determinism — given the location of every particle in the universe and enough computing power we could predict the universe perfectly. However it was the disconnect between the perfection of nature and our human imperfections in measuring and understanding it that led to Laplace’s involvement in a theory based on probabilism.
Laplace was frustrated at the time by astronomical observations that appeared to show anomalies in the orbits of Jupiter and Saturn — they seemed to predict that Jupiter would crash into the sun while Saturn would drift off into outer space. These prediction were, of course, quite wrong and Laplace devoted much of his life to developing much more accurate measurements of these planets’ orbits. The improvements that Laplace made relied on probabilistic inferences in lieu of exacting measurements, since instruments like the telescope were still very crude at the time. Laplace came to view probability as a waypoint between ignorance and knowledge. It seemed obvious to him that a more thorough understanding of probability was essential to scientific progress.
The Bayesian approach to probability is simple: take the odds of something happening, and adjust for new information. This, of course, is most useful in the cases where you have strong prior knowledge. If your initial probability is off the Bayesian approach is much less helpful.
Includes a link to Eliezer Yudkowsky's intuitive explanation of the theorem and this Quora response to the question “What does it mean when a girl smiles at you every time she sees you?” which are both excellent.
A Bayesian approach to life is a sensible one, but the human mind isn't optimized to apply the theory accurately except at the broadest of levels (most people's intuition is way off when it comes to the mammogram example used in both the overview and the Yudkowsky piece linked above). This can be particularly problematic when it comes to our judgments of other people; we overweight new information without considering the prior odds. This is exacerbated by the internet, where we are prone to judge others on the select few pieces of content they choose to post for public consumption.