According to my perhaps naive interpretation of that, the "degree of surprise" would depend on at least three things:

1. the laws of nature (i.e. how accurately do the laws of physics permit measuring the system and how determined are future states based on current states)

2. one's present understanding of the laws of nature

3. one's ability to measure the state of a system accurately and compute the predictions in practice

It strikes me as odd to include 2 and 3 in a definition of "entropy."