Ah, I think I got it. The point of the exercise is not to formulate the concept of "amount of suprise (∝ amount of information gained) IN CASE the event happens

Ah, I think I got it. The point of the exercise is not to formulate the concept of "amount of suprise (∝ amount of information gained) IN CASE the event happens" but the "EXPECTED amount of entropy gain", for us to know before it happens. That's why we need to take a middle ground between very common events that aren't surprising, and gain us hardly anything, and rare events that gain us a lot of information, but happen so rarely that they don't matter a whole lot. The formula derived here manages to find the balance between these two extremes.