I'm studying (relativistic) quantum field theory and have a very simple question. Take for example the real scalar field. My notes simply state that <0|0>=1 is a very natural normalisation. If I'm not mistaken, then this implies that the probability of measuring the vacuum state is 1. How is this to be interpreted? If the field has an infinite number of states then will the probabilities add up to an infinite number? Does a probability greater than one correspond to the measurement of more than one particle? I think not because multiple particles correspond to a single state. Basically, I don't understand how the normalisation of states is to be interpreted in quantum field theory. Can anyone help?