However, there is not a considerable difference between this number and the number of weights and thresholds that have to be 'known' in order to build a neural network, and these can only be learned by training. It is an enormous weakness of neural networks that you are unable to utilize the knowledge you might have in advance. Probabilities, on the other hand, can be assessed using a combination of theoretical insight, empiric studies independent of the constructed system, training and various more or less subjective estimates. Finally it should be mentioned that in the construction of a neural network the route of inference is fixed. It is decided in advance, about which relations information is gathered, and which relations the system is expected to calculate.
Bayesian networks are much more flexible in that respect.