WHAT IS PROBABILITY?

A third quote by Schrödinger summarizes the first two and clarifies what we are talking about:

“ Given the state of our knowledge about everything that could possibly have any bearing on the coming true. . . the numerical probability $p$ of this event is to be a real number by the indication of which we try in some cases to setup a quantitative measure of the strength of our conjecture or anticipation, founded on the said knowledge, that the event comes true  (6)

Probability is not just “a number between 0 and 1 that satisfies some basic rules” (`the axioms'), as we sometimes hear and read, because such a `definition' says nothing about what we are talking about. If we can understand probability statements it is because we are able, so to say, to map them in some `categories' of our mind, as we do with space and time (although for values far from those we can feel directly with our senses we need some means of comparison, as when we say “30 times the mass of the sun”, and rely on numbers).

Think for example of two generic events $E_1$ and $E_2$ such that $p_1=P(E_1\,\vert\,I)$ and $p_2=P(E_2\,\vert\,I)$. Imagine also that we have our reasons - either we have evaluated the numbers, or we trust somebody's else evaluations - to believe that $p_1$ is much larger that $p_2$, where `much' is added in order to make our feeling stronger. It is then a matter of fact that: “the strength of our conjecture” strongly favors $E_1$; we expect (“anticipate”) $E_1$ much more than $E_2$; we will be highly surprised if $E_2$ occurs, instead of $E_1$.Or, in simpler words, we believe $E_1$ to occur much more than $E_2$.