As Wikipedia says, the above is a particular _interpretation_, not a _definition_ of probability. If you'd take it as a definition, you'd not be able to derive the slightest thinghttp://en.wikipedia.org/wiki/Bayesian_probability "Bayesian probability interprets the concept of probability as 'a measure of a state of knowledge', in contrast to interpreting it as a frequency or a 'propensity' of some phenomenon."
As I said before, a Bayesian definition of probability does depend on knowledge. I don't know why you bother asserting the contrary when it is such a widely-known definition of probability.
The subjective interpretation may be legitimate to guide actions, but it is not science.
I have been using successfully Bayesian methods without this concept of Bayesian probability, in an objective context.