Data analysis encompasses a spectrum of tasks, from high-level conceptual reasoning to lower-level execution. While AI-powered tools increasingly support execution tasks, there remains a need for intelligent assistance in conceptual tasks. This paper investigates the design of an ordered node-link tree interface augmented with AI-generated information hints and visualizations, as a potential shared representation for hypothesis exploration. Through a design probe (n=22), participants generated diagrams averaging 21.82 hypotheses. Our findings showed that the node-link diagram acts as "guardrails" for hypothesis exploration, facilitating structured workflows, providing comprehensive overviews, and enabling efficient backtracking. The AI-generated information hints, particularly visualizations, aided users in transforming abstract ideas into data-backed concepts while reducing cognitive load. We further discuss how node-link diagrams can support both parallel exploration and iterative refinement in hypothesis formulation, potentially enhancing the breadth and depth of human-AI collaborative data analysis.