When you try to figure something out, you rarely start from zero. You begin with a hunch, an initial guess based on everything you already know. This is the foundation of Bayesian thinking — it's a structured way of updating your beliefs as you get new information. The first step is always acknowledging your starting point.

Think of a prior probability as your personal, subjective starting line. It's not pulled out of thin air. It’s shaped by your past experiences, general knowledge, and common sense. If you live in London and wake up to a grey, overcast sky in November, your experience tells you there's a good chance of rain. That initial assessment, before you check a detailed weather forecast, is your prior belief.

To make these beliefs useful, we need to assign them a value. This might sound complicated, but it's something we do intuitively all the time. We can express these initial guesses as percentages or fractions. For example, based on those grey London clouds, you might feel there's an 80% chance of rain. That 80% (or 0.8) is your prior probability.

Let's try another example. Imagine your friend sneezes. What's the first thing you think of? Most likely, a common cold. Your prior probability that they have a cold is quite high. Your prior probability that they have a rare, tropical illness is extremely low. Why? Because your background knowledge tells you that colds are incredibly common, while tropical diseases are, well, rare where you live.

Assigning a number makes the belief concrete. It gives us a solid value we can work with later. A high number, like 90% (0.9), means you have a strong initial belief that something is true. A low number, like 5% (0.05), means you think it's very unlikely. A 50% (0.5) prior means you're completely unsure, giving it even odds.

It's important to remember that this is just the beginning. The prior probability isn't the final answer. It’s a flexible starting point designed to be updated as you gather more specific facts and evidence . This process of updating is the next step in our journey.