Let $x$ be the probability that a snowflake picked from the ground is a 'Stellar Dendrite'. Thus, when a new snowflake is falling, the last snowflake was Stellar Dendrite with probability $x$.

This means that the probability the new falling snowflake is Stellar Dendrite $= x*p + (1-x)*q$. But, for the composition of the snowflakes on the ground to remain constant, $xp+(1-x)q$ should be same as $x$

$\implies x = xp + q - xq = x(p-q) + q$

$\implies x (1- (p-q)) = q$

$\implies x = \dfrac{q}{ (1- p + q)}$

This is a kind of steady state analysis.