Overall definition:

A measure for representing or expressing uncertainty, variation or beliefs, following the rules of probability calculus.

Different types/interpretations:

Classical probability: The classical interpretation applies only in situations with a finite number of outcomes which are equally likely to occur: The probability of A is equal to the ratio between the number of outcomes resulting in A and the total number of outcomes, i.e.

P(A) = Number of outcomes resulting in A / Total number of outcomes

Propensity/frequentist probability: A frequentist probability of an event A, denoted P_f(A), is defined as the limiting fraction of times the event A occurs if the situation considered were repeated (hypothetically) an infinite number of times. The propensity interpretation holds that the probability is to be thought of as a physical characteristic; a propensity of a repeatable experimental set-up which produces outcomes with limiting relative frequency probability P_f(A)
Subjective (judgmental, knowledge-based) probability:
1. Reference to an uncertainty standard: The probability P(A) is the number such that the uncertainty about (degree of belief in) the occurrence of A is considered equivalent by the person assigning the probability, to the uncertainty about (degree of belief in) some standard event, for example drawing at random a red ball from an urn that contains P(A) x 100% red balls.
2. Betting and related type of interpretations: The probability of an event A is the price at which the person assigning the probability is neutral between buying and selling a ticket that is worth one unit of payment if the event occurs, and worthless if not.

Frequentist probabilities are in general unknown and must be estimated.

Likelihood: The same as probability.

Chance: In a broad sense the same as probability. In a technical Bayesian context, a chance is the limit of the frequency in an exchangeable, infinite Bernoulli series (the Bayesian equivalent of a frequentist probability).

Frequency:

Number of events per unit of measurement of the related physical dimension considered (most commonly time)
Expected number of such events