[kjhcvkek77]

I appreciate your response but I don't really agree. They say that likelihood can be multiplied by any scale factor or that it's only the comparative difference that matters, or we can make a little plot, but they don't actually explain why.

I can try to make an explanation from the bayesian framework(but as I mentioned it's not the only relevant one)

Likelihood is P(measurement=measurement'|parameter=parameter'). This is a small value. Given a prior we can P(parameter=parameter'|measurement=measurement'). This is also small. But when we compute P(parameter'-k<parameter<parameter'+k|measurement=measurement') then all the smallness cancels see the formulation of bayes that reads

P(X_i|Y) = (P(X_i)P(Y|X_i)/(sum_j P(X_j)P(Y|X_j))

I'm obviously skipping a lot of steps here because I'm sketching an explanation rather than giving one.