Maximum entropy probability distribution

Imagine it's snack time and you have a bunch of different snacks to choose from. You want to choose a snack, but you don't have a specific preference for any of the snacks - you just want to choose one that is most likely to make you happy.

Now, let's say you have a friend who knows what snacks you like and can rate them on a scale from 1 (worst) to 10 (best). Your friend can also tell you how likely you are to enjoy each snack based on your past snack choices.

If your friend rates all the snacks and gives a probability score to each snack, that's how you can find the maximum entropy probability distribution. The entropy is a fancy way of measuring how spread out the possibilities are. If all the snacks have the same rating and chance of making you happy, there is a lot of entropy because the possible outcomes are spread out evenly. On the other hand, if there is one snack that is highly rated and likely going to make you happy, there is less entropy because there is less possibility for other snacks.

The maximum entropy probability distribution is the most likely set of probabilities for any given set of ratings and information about your past preferences. It's like your friend is giving you the most "fair" chance of choosing a snack you'll like without having any specific preferences.