1. A computer-implemented method for diagnosing faults across a plurality of hosts in a complex multi-host environment comprising: for each host in the complex multi-host environment, determining a probability that a problem occurred on said each host based on a probabilistic model that corresponds to said each host; wherein the probabilistic model for said each host defines: a) a cause-effect relationship between one problem and another problem of one or more system problems that can occur on said each host; and b) for each problem of the one or more system problems, the probability that said each problem has occurred on said each host; wherein the probabilistic model for said each host is expressed at least in part as nodes and directed connections to nodes in a directed acyclic graph (DAG); wherein a node represents a problem of the one or more system problems, and is associated with a probability of failure value and a threshold value, wherein the probability of failure value associated with the node reflects the probability that the problem represented by the node has occurred on said each host; wherein the probabilistic model for said each host includes a system failure node that represents a probability that a failure occurred in said each host; determining, based on a probability of failure value and a threshold value associated with the system failure node in the probabilistic model corresponding to a first host, that a problem occurred on the first host; examining each probabilistic model corresponding to each host of the plurality of hosts in the complex multi-host environment to identify a set of potential root cause nodes across the plurality of hosts, wherein each potential root cause node of the set of potential root cause nodes is identified based on a probability of failure value and a threshold value that are associated with said each potential root cause node; selecting from the set of potential root cause nodes a particular root cause node, in the probabilistic model corresponding to a second host, based on the probability of failure value associated with the particular root cause node; identifying as a symptom node, a system failure node in the probabilistic model corresponding to the second host; generating an explanation for the problem that occurred on the first host by identifying a path through a DAG between the particular root cause node and the symptom node of the second host; wherein the DAG expresses the probabilistic model corresponding to the second host; and wherein the method is performed by one or more computing devices.