Probability of the causes

Generally speaking, what is missing in the usual theory of probability is the crucial concept of probability of hypotheses and, in particular, probability of causes: ``the essential problem of the experimental method'' (Poincaré):

``I play at écarté with a gentleman whom I know to be perfectly honest. What is the chance that he turns up the king? It is 1/8. This is a problem of the probability of effects. I play with a gentleman whom I do not know. He has dealt ten times, and he has turned the king up six times. What is the chance that he is a sharper? This is a problem in the probability of causes. It may be said that it is the essential problem of the experimental method''[6].
``...the laws are known to us by the observed effects. Trying to deduct from the effects the laws which are the causes, it is solving a problem of probability of causes''[7].

A theory of probability which does not consider probabilities of hypothesis is unnatural and prevents transparent and consistent statements about the causes which may have produced the observed effects from being assessed.