Randomness and probability are two differnet concepts: probaility is a measure (according to measure theory) which measures the randomness. Randomness is the object to be measured by probability. For example, probability is a mapping from randomness to the real number between 0 and 1. The similar examples are that the entropy measures the uncertanity; product of length and width measures the area of rectangle etc. Please see “A mathematical theory of ability measure” by N. Kong ets for more examples to answer this question.

]]>