There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies (full) termination or when runtime complexity and innermost runtime complexity coincide. We adapt these criteria to the probabilistic setting, e.g., we show when it suffices to analyze almost-sure termination w.r.t. innermost rewriting in order to prove (full) almost-sure termination of probabilistic term rewrite systems. These criteria can be applied for both termination and complexity analysis in the probabilistic setting. We implemented and evaluated our new contributions in the tool AProVE. Moreover, we also use our new results to investigate the modularity of probabilistic termination properties.