Let $c_i$ be the center of a micro-cluster (i.e. we have many centers representing some fragments of clusters). Let $c_1$ be the center which is the closest to a new data-point $x$, such that $d_{x,c_1} = distance(x, c_1)$.
(1) Is it possible to express d by a probability $d_{x,c_1}$ by a probability $p_{x,c_1}$ which tends to 1 as $d_{x,c_1}$ is higher, and to 0 as $d_{x,c_1}$ is smaller ? I think it is more intuitive to manipulate a probability instead of a distance.
(2) Same question as (1), however this time I suppose that $p_{x,c_1} = 0$ if $d_{x,c_1} < radius$.