Search engine companies collect the "database of intentions", the histories of their users' search queries. These search logs are a gold mine for researchers. Search engine companies, however, are wary of publishing search logs in order not to disclose sensitive information. In this paper we analyze algorithms for publishing frequent keywords, queries and clicks of a search log. We first show how methods that achieve variants of $k$-anonymity are vulnerable to active attacks. We then demonstrate that the stronger guarantee ensured by $ε$-differential privacy unfortunately does not provide any utility for this problem. We then propose an algorithm ZEALOUS and show how to set its parameters to achieve $(ε,δ)$-probabilistic privacy. We also contrast our analysis of ZEALOUS with an analysis by Korolova et al. [17] that achieves $(ε',δ')$-indistinguishability. Our paper concludes with a large experimental study using real applications where we compare ZEALOUS and previous work that achieves $k$-anonymity in search log publishing. Our results show that ZEALOUS yields comparable utility to $k-$anonymity while at the same time achieving much stronger privacy guarantees.