How does one obtain the normalising constant in the following context?

Question

Define the migration kernel $$p(x,y) := \frac{1}{N_{M}} \sum_{k \geq ||x-y|| } \frac{1}{M^{2k-1}}, $$ and define the distance metric $$||x-y|| := \min \{ k \in \mathbb{N}_{0} : x_{l} = y_{l} \quad \forall l > k \} $$ on the hierarchical lattice $$ \Omega_{M} := \Big{\{} x = (x_{k})_{k \in \mathbb{N}} : x_{k} \in \{ 0, 1, \dots , M-1 \} , \sum_{k \in \mathbb{N}} x_{k} < \infty \Big{\}}. $$ How does one show that $N_{M} = M^{2} / (M^{2} -1) $ ? I suspect it has to do with summing over the migration kernel somehow and that the sum must be equal to one. However, I'm not quite sure what kind of sum I should take to find the value of the normalising constant $N_{M}$.