The so-called Copenhagen Interpretation is not a single interpretation but a collection with some common ground. The entities it pre-supposes are particles, fields or potentials, time, space and measuring devices. It is not a subjective interpretation, in the sense that the outcomes of experiments do not depend on the views or beliefs of the experimenter. Particles have 'observable' properties such as position, momentum and spin (observable really means measurable), but the values of those properties are the results of measurements, ie of the interaction between the particle and the measuring device. Importantly, certain properties cannot have precisely defined values simultaneously. For example, when a particle has a well-defined position, it does not have a well-defined momentum, and vice versa.
The interpretation assumes that every particle has an associated 'wave function', which is a function of position and time. The magnitude of the wave function at any point in space indicates the probability that a measurement will localise the particle at that point. Note that the interpretation does not assume that the particle actually is at a point before its location is measured, or that the particle is found at that point by the measuring device- instead it assumes that the act of measurement plays a role in causing the particle to be at the measured location.
More generally, the interpretation assumes that when a property of a particle is measured, the wave function of the particle is changed by the measurement to become one of an allowed set of 'eigenfunctions' associated with the property being measured. The details of this are too complicated to describe here, but the way it works is truly striking once you understand it. Each of the allowed eigenfunctions of one measurable property A may be expressed as a sum of the eigenfunctions of another of the particle's measurable properties B. If a particle is in a particular eigenstate of A, and you subject it to a measurement of B, the particle's wave function will jump in an indeterministic way to become one of the eigenfunctions of B. The probability of it jumping to a specific one of the eigenfunctions of B depends on the extent to which that eigenfunction figured in the expansion of the pre-measurement eigenfunction of A.
In short, the probabilistic nature of quantum mechanics has nothing to do with beliefs. The key equations of quantum mechanics give you the probability that a particle in one specific quantum state will change to another specific quantum state as a consequence of a measurement.