Probability that a random bridge board does not contain a sequence? Two cards with adjacent values and the same suit produce a SEQUENCE. For example,
the heart-ten and the heart-jack form a sequence. The order of the values in
bridge is $$23456789TJQKA$$

-What is the probability that a random bridge board contains no sequence in any
 hand ? (That means, for example : If North holds the queen of spades, he neither
 holds the jack nor the king of spades )

A long time ago, I approached this problem by first determining all possible
combinations not containing a sequence (for example kt742) , and then calculate
the number of boards from that. I remember that the probability is very low.
But there should be a better method, perhaps inclusion-exclusion or something
like that.
if i get your question right,
an ideal sample set E will be a set of all subsets
E={S2,S3,S4,…,S12}

whereas is subset of three serial number s=[n-1,n,n+1]

your sample space for all possible options are equal 2^11 
one of these event meet the required criteria which is  ‘E' in your case.
the probability of having Pr(E=1) = 1/(2^11) 

hope it helps
if i get your question right,
an ideal sample set E will be a set of all subsets
E={S2,S3,S4,…,S12}

whereas is subset of three serial number s=[n-1,n,n+1]

your sample space for all possible options are equal 2^11 
one of these event meet the required criteria which is  ‘E' in your case.
the probability of having Pr(E=1) = 1/(2^11) 

hope it helps