I want to write the following sentence formally:
The sequence $S$ contains elements of the set $A$. The probability value $P(a)$ for an element $a$ is defined as the number of its occurrences in the sequence $S$, divided by the count of all its elements.
I can write it the following manner:
$$ S = (s_1, s_2, ..., s_n) : s_i \in A.$$ $$ P(a) := {{ \left| \lbrace i \in \lbrace 1, 2, ..., n \rbrace : s_{i} = a \rbrace \right| } \over {n}}, \text{ given } n > 0\text{ and }a \in A. $$
It's, however, quite long and rather not elegant. Is there a simpler way to write this?
Edit:
There's always a solution, which involves breaking the formula to smaller parts:
$$ \text{Let } C(x) = \left| \lbrace i \in \lbrace 1, 2, ..., n \rbrace : s_i = x \rbrace \right|.$$ $$ P(a) := {C(a) \over n}. $$
It's more readable, but it's still not what I'm searching for...