diff --git a/litellm/router_strategy/capability_router/policy.py b/litellm/router_strategy/capability_router/policy.py
index d76a831e9d3..46303211704 100644
--- a/litellm/router_strategy/capability_router/policy.py
+++ b/litellm/router_strategy/capability_router/policy.py
@@ -43,7 +43,7 @@ def select_capability_model(
     verdict: CapabilityClassifierVerdict,
     estimated_costs: Mapping[str, float | None],
 ) -> CapabilityRoutingDecision:
-    """Choose the cheapest candidate at or above the configured probability."""
+    """Choose the cheapest candidate above the configured probability."""
     configured_models = tuple(candidate.model for candidate in config.candidates)
     scores = {candidate.model: candidate for candidate in verdict.candidates}
     if set(scores) != set(configured_models):
@@ -55,7 +55,7 @@ def select_capability_model(
             p_solve=scores[model].p_solve,
             reason=scores[model].reason,
             estimated_cost=estimated_costs.get(model),
-            qualified=scores[model].p_solve >= config.probability_threshold,
+            qualified=scores[model].p_solve > config.probability_threshold,
         )
         for model in configured_models
     )
diff --git a/tests/test_litellm/router_strategy/capability_router/test_capability_router.py b/tests/test_litellm/router_strategy/capability_router/test_capability_router.py
index fd3fee10c5e..2c2879252cd 100644
--- a/tests/test_litellm/router_strategy/capability_router/test_capability_router.py
+++ b/tests/test_litellm/router_strategy/capability_router/test_capability_router.py
@@ -84,6 +84,22 @@ def test_policy_falls_back_if_no_model_qualifies_or_price_is_unknown() -> None:
     )
 
 
+def test_probability_must_be_strictly_above_threshold() -> None:
+    parsed = CapabilityRouterConfig.model_validate(config())
+    verdict = CapabilityClassifierVerdict.model_validate(
+        {
+            "candidates": [
+                {"model": "small", "p_solve": 0.7, "reason": "on the boundary"},
+                {"model": "frontier", "p_solve": 0.7, "reason": "on the boundary"},
+            ]
+        }
+    )
+
+    assert select_capability_model(parsed, verdict, {"small": 0.01, "frontier": 0.05}).reason == (
+        "no_qualified_candidate"
+    )
+
+
 def test_router_registers_capability_strategy() -> None:
     router = Router(
         model_list=[