Crow & Kimura. 1970. Introduction to Population Genetics Theory. p. 65.

Genotype      Frequency

AA                p^2*(1-f) + p*f

Aa                2pq(1-f)

aa                q^2*(1-f) + q*f

f is the inbreeding coefficient. With f=0 you have the standard HW proportions. With f=1 there are no heteozygous Aa.

Dear Thanasis

There are many assumptions for HW equilibrium, from these assumptions that the population must be a large number ( Hundreds rather than tens) and the random mating, while the inbreeding occurs in a small closed population and controlled mating.

So, I think this probability (HWE and inbreeding) not found in the real world.

Good Luck

Crow & Kimura. 1970. Introduction to Population Genetics Theory. p. 65.

Genotype      Frequency

AA                p^2*(1-f) + p*f

Aa                2pq(1-f)

aa                q^2*(1-f) + q*f

f is the inbreeding coefficient. With f=0 you have the standard HW proportions. With f=1 there are no heteozygous Aa.

To sum up, HWE assumes panmixia. In case of inbreeding, you do not have random mating so in theory, HWE is no longer applicable. 

As it is well known, H-W equilibrium in a population holds good if there is no mutation, and absence of population structure (or random mating), and the population is large enough. The population structure include all the variables which influences the gene frequency -- e.g. migration, marriage all the rules conditioned or imposed (or followed by) culture and society. 

     Since inbreeding is a (preferential) marriage practice, where the couples are (genetically) related by blood (please note that blood is English usage that we still follow with reference to family hereditary relationships) through blood is nothing to do with family relationship) is obviously  not random mating one of the condition required for H-W law to hold. Hence inbreeding does change the change the gene frequency, so HW will not hold at least for those loci which are influenced by inbreeding. 

       Therefore, as Dr. Mauro Santos has pointed out the theoretical results obtained by Crow and Kimuara (1970), in a population where there is inbreeding or inbreeding is practiced, over time, there will be loss of hetero-zygotes over generations leading to fixation of homo-zygotes in the long run. The amount of loss of hetero-zygotes can be estimated using the Crow and Kimuras' formula. The effect of inbreeding on gene frequency in  population is-- what is called as "inbreeding load". This is related to some of the deleterious genes, especially in recessive inheritance  that might get a chance to get express in homo-zygote state as a result of inbreeding. Indeed, in the long run, in a population practicing inbreeding over generation, the deleterious genes gets eliminated in the population since as per Darwin's natural selection hypothesis such individuals will possibly die -- a 'genetic death'  -- without a chance to pass on their genes to the next generation.

         But one should be careful also, since what is theoretical expectation, may not be practically possible to realize in empirical situation. There are several reasons for the variance between theory and empirical situations. Primarily in a population gene frequency is influenced by several factors, where inbreeding could be one factor. it is also difficult to control other factors that influence the gene frequency and look for only due to inbreeding alone. Theoretically we do not have expectations in case of a gene frequency influenced by several factors. And practically it is also not easy to study inbreeding in a population by pedigree method -- generally one takes close marriages at first generation level. It is because the the inbreeding over generations gets diluted and supposedly with least effect.  There are other practical problems related to population culture etc which makes a researcher to obtain or estimate the inbreeding coefficient. 

        Indeed, inbreeding studies conducted world wide show variant results -- some studies show the effect of inbreeding effect and other studies do not show the congruence results. The popular Schull and Neel study in early and late 1970 in Japan has shown no perceivable effect of inbreeding for the loci that they examined. 

  But the story in case of polygenic characters is somewhat different - this is referred as 'inbreeding effect'. There are some good examples of effect of inbreeding on some of the polygenic characters -- e.g., anthropometric characters or dermatoglyphic characters. In case of polygenic characters, there will be decrease in mean and variance proportional to inbreeding coefficient (the estimate to measure the amount of inbreeding in a population -- which is based on different types of consanguineous marriages that takes places or occurs. 

          Having said all those related to inbreeding and its effects as above,  one should also remember that marriage is primarily a phenotypic by choice -- one prefers his or her marriage partner based on physical characters and social and cultural preferences -- we do not marry by looking at the genetic profile of a person -- unless in some known cases of deleterious genes -- e.g . HbE, or HbS, etc where one avoids marrying a person who is carrier of Hbs type for example. Since marriage is blind to the genetic status or profile of a person, these loci are virtually come under random mating. Therefore seen in the perspective of H-W law, these loci do follow HW equilibrium. In practice for several of the loci that we test, routinely we do check for HW test and several of them follow HW law irrespective of population structure variables.