Expose it to tests. For example, you might stick your head out a window and look up. The theory that the sky is green strongly predicts that you should see green and only very weakly allows for you to see anything else (your eyes may occasionally play tricks on you, perhaps you are looking close to a sunset, etc.).
2) How can I assign a probability to it to test its degree of truthfulness?
3) How can I update this belief?
If you knew absolutely nothing about skies other than that they were some colour, you would start with a symmetrical prior distributed across a division of colour space. You would then update your belief every time you come into contact with entangled information. For example, every time you look up at the sky and see a colour, your posterior probability that the sky is that colour goes up at the expense of alternative colours. Observing other people describe what they see when they look at the sky and learning about how vision works and the chemical composition of the sky are also good examples of evidence you could use.
In practise, manually updating every belief you have all the time is far to arduous, and most people collect large amounts of beliefs and information prior to learning much about statistics anyway. Because of this, the prior probability you assign to your beliefs will often have to be a quick approximation.
Expose it to tests. For example, you might stick your head out a window and look up. The theory that the sky is green strongly predicts that you should see green and only very weakly allows for you to see anything else (your eyes may occasionally play tricks on you, perhaps you are looking close to a sunset, etc.).
If you knew absolutely nothing about skies other than that they were some colour, you would start with a symmetrical prior distributed across a division of colour space. You would then update your belief every time you come into contact with entangled information. For example, every time you look up at the sky and see a colour, your posterior probability that the sky is that colour goes up at the expense of alternative colours. Observing other people describe what they see when they look at the sky and learning about how vision works and the chemical composition of the sky are also good examples of evidence you could use.
In practise, manually updating every belief you have all the time is far to arduous, and most people collect large amounts of beliefs and information prior to learning much about statistics anyway. Because of this, the prior probability you assign to your beliefs will often have to be a quick approximation.