1. A computer-implemented method for finding one or more most-probable fault cause paths of a problem symptom in a multi-host system comprising: detecting at least one system problem of one or more system problems of said multi-host system based on a probabilistic model of causes and effects of problems in said multi-host system; wherein said probabilistic model defines: a) a cause-effect relationship between one problem and another problem of the one or more system problems of said multi-host system; b) for each problem of the one or more system problems of said multi-host system, a probability that said each problem has occurred in said multi-host system; wherein said probabilistic model is expressed at least in part as nodes and directed connections in a directed acyclic graph (DAG); wherein a node represents a problem of the one or more system problems, and a probability of failure value is associated with the node, wherein the probability of failure value associated with the node reflects a probability that the problem represented by the node has occurred in said multi-host system; wherein the probability of failure value associated with the node is computed as an aggregation function over a set of probability of failure values, wherein each probability of failure value of the set of probability of failure values is associated with a time point of a plurality of successive time points in a recent time interval; wherein each directed connection of the directed connections leads from a first node to a second node; wherein the first node represents a first problem in said multi-host system; wherein the second node represents a second problem in said multi-host system, and wherein the first problem causes the second problem; selecting for diagnosis a particular problem of the at least one detected system problems; identifying as a symptom node, a node representing the particular problem selected for diagnosis; identifying as included in a set of potential root cause nodes, each root cause node for which there is a path in the DAG from said each root cause node to the symptom node; wherein a path in the DAG exists between a source node and a target node if starting at the source node, a set of one or more directional links may be traversed in sequence that lead to the target node; wherein a root cause node is not a target node for any path in the DAG; comparing the probability of failure value associated with each potential root cause node of the set of potential root cause nodes; selecting from the set of potential root cause nodes a particular root cause node associated with a highest probability of failure value among all probability of failure values associated with said each potential root cause node; and identifying a most likely path in the DAG between the particular root cause node and the symptom node, wherein identifying the most likely path is based on probability of failure values associated with nodes that lie on a path between the particular root cause node and the symptom node.