Relational databases are foundational to numerous domains, including business intelligence, scientific research, and enterprise systems. However, accessing and analyzing structured data often requires proficiency in SQL, which is a skill that many end users lack. With the development of Natural Language Processing (NLP) technology, the Text-to-SQL systems attempt to bridge this gap by translating natural language questions into executable SQL queries via an automated algorithm. Yet, when operating on complex real-world databases, the Text-to-SQL systems often suffer from ambiguity due to natural ambiguity in natural language queries. These ambiguities pose a significant challenge for existing Text-to-SQL translation systems, which tend to commit early to a potentially incorrect interpretation. To address this, we propose an interactive Text-to-SQL framework that models SQL generation as a probabilistic reasoning process over multiple candidate queries. Rather than producing a single deterministic output, our system maintains a distribution over possible SQL outputs and seeks to resolve uncertainty through user interaction. At each interaction step, the system selects a branching decision and formulates a clarification question aimed at disambiguating that aspect of the query. Crucially, we adopt a principled decision criterion based on Expected Information Gain to identify the clarification that will, in expectation, most reduce the uncertainty in the SQL distribution.