Current intrusion detection systems (IDSs) can only discover single-step attacks but not complicated multi-stage attacks. Therefore, it is not only important, but also challenging for security managers to correlate security alerts with specific patterns to predict a multi-stage attack. In this paper, we propose Judge Evaluation of Attack intensioN (JEAN), which inspects the security alerts in the network and provides a probabilistic approach for the projection of the multi-stage attack by measuring the difference between the stored and the actual multi-stage attack session graphs (ASG). The experimental results show that JEAN is able to project possible attacks with more accuracy than Longest Common Subsequence (LCS) based approaches on DARPA 2000 and DARPA GCP (Grand Challenge Problem) specific attack scenario datasets.