  We consider both analytically and numerically creation conditions of diverse
hierarchical trees. A connection between the probabilities to create
hierarchical levels and the probability to associate these levels into united
structure is found. We argue a consistent probabilistic picture requires making
use of the deformed algebra. Our consideration is based on study of main types
of hierarchical trees, among which both regular and degenerate ones are studied
analytically, while the creation probabilities of the Fibonacci and free-scale
trees are determined numerically. We find a general expression for the creation
probability of an arbitrary tree and calculate the sum of terms of deformed
geometrical progression that appears at consideration of the degenerate tree.
