In this short paper an approach to the ATM hierarchical (PNNI) routing issue is presented based on a simple algorithm that chooses a route for a connection request out of a predefined list of possible routes between a specific source-destination pair in a probabilistic way. A route fitness (cost) function is used to assign selection probabilities to every candidate path and arriving connection requests are routed independently according to these path probabilities. This cost function has been chosen in a way to achieve a successful trade-off between the use of minimum-hop routes and the application of the load-balancing concept. Moreover we show that the performance of the proposed algorithm and other probabilistic routing algorithms can be enhanced with the application of scaling techniques that are used in genetic algorithms (GAs) maximizing the network revenue. Simulation results over a wide range of uniform, time-varying and skewed loading conditions show the effectiveness of the proposed routing algorithm.