We consider a probabilistic knowledge base represented by a conditional probability assessment on an arbitrary finite family of conditional events. Following the approach of de Finetti to conditional events, we use the concept of generalized atom to introduce a suitable matrix representing the truth values of the given conditional events. Moreover, we prove some theoretical results, by means of which using the linear programming technique a procedure to check the probabilistic consistency of the given knowledge base can be easily constructed. Finally, a simple example is examined.