Web search engines (e.g., Google, Bing, Qwant, and DuckDuckGo) may process a myriad of search queries per second. According to Internet Live Stats, Google handles more than two hundred million queries per hour, i.e., about two trillion queries per year. For monetization purposes, the queries can be stored and complemented with additional data, referred to as query logs. Together, they can correlate valuable information to build accurate user profiles. Before releasing the query logs to third parties (e.g., for profit purposes), the personal information contained in the query logs must be properly protected by the web search engines. Current regulations establish strict control, and require from provable anonymization processing (e.g., in terms of statistical disclosure) of any personally identifiable information. In this paper, we tackle this challenge. We propose a real-time anonymization solution to protect streams of unstructured data at the server side. Our approach is based on the use of a probabilistic k-anonymity technique. It allows probabilistic processing of personally identifiable attributes contained in the query logs, with provable privacy properties. Our solution handles limitations of traditional k-anonymity approaches with respect to unstructured data and real-time processing. We present the implementation of our solution and report experimental evaluation results. The evaluation is conducted in terms of privacy, utility, and scalability achievement. Results validate the feasibility of our proposal.