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We formally show that as probability concentrates on the top-$1$ candidate, the expected number of distinct responses collapses to one regardless of the sampling budget $K$. This theoretical implication is further verified by our empirical tracking of top-$N$ candidate probabilities during training, where the top-$1$ candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: \\emph{preserving non-negligible probability mass on the top-$N$ candidates}. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. 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