diff --git a/src/EFCore.PG/Query/ExpressionTranslators/Internal/NpgsqlArrayMethodTranslator.cs b/src/EFCore.PG/Query/ExpressionTranslators/Internal/NpgsqlArrayMethodTranslator.cs
index e128dacea9..847da4c171 100644
--- a/src/EFCore.PG/Query/ExpressionTranslators/Internal/NpgsqlArrayMethodTranslator.cs
+++ b/src/EFCore.PG/Query/ExpressionTranslators/Internal/NpgsqlArrayMethodTranslator.cs
@@ -141,7 +141,10 @@ static bool IsMappedToNonArray(SqlExpression arrayOrList)
                             "array_position",
                             [array, item],
                             nullable: true,
-                            TrueArrays[2],
+                            // array_position can return NULL even if both its arguments are non-nullable;
+                            // this is currently the way to express that (see
+                            // https://github.com/dotnet/efcore/pull/33814#issuecomment-2687857927).
+                            FalseArrays[2],
                             arrayOrList.Type),
                         _sqlExpressionFactory.Constant(1)),
                     _sqlExpressionFactory.Constant(-1));
@@ -161,7 +164,10 @@ static bool IsMappedToNonArray(SqlExpression arrayOrList)
                             "array_position",
                             [array, item, startIndex],
                             nullable: true,
-                            TrueArrays[3],
+                            // array_position can return NULL even if both its arguments are non-nullable;
+                            // this is currently the way to express that (see
+                            // https://github.com/dotnet/efcore/pull/33814#issuecomment-2687857927).
+                            FalseArrays[3],
                             arrayOrList.Type),
                         _sqlExpressionFactory.Constant(1)),
                     _sqlExpressionFactory.Constant(-1));
diff --git a/src/EFCore.PG/Utilities/Util.cs b/src/EFCore.PG/Utilities/Util.cs
index bdbceb2829..97bca187c1 100644
--- a/src/EFCore.PG/Utilities/Util.cs
+++ b/src/EFCore.PG/Utilities/Util.cs
@@ -15,5 +15,10 @@ internal static class Statics
         [true, true, true, true, true, true, true, true]
     ];
 
-    internal static readonly bool[][] FalseArrays = [[], [false], [false, false]];
+    internal static readonly bool[][] FalseArrays = [
+        [],
+        [false],
+        [false, false],
+        [false, false, false]
+    ];
 }
diff --git a/test/EFCore.PG.FunctionalTests/Query/ArrayArrayQueryTest.cs b/test/EFCore.PG.FunctionalTests/Query/ArrayArrayQueryTest.cs
index 2b481dfcd5..cbe860667c 100644
--- a/test/EFCore.PG.FunctionalTests/Query/ArrayArrayQueryTest.cs
+++ b/test/EFCore.PG.FunctionalTests/Query/ArrayArrayQueryTest.cs
@@ -835,7 +835,7 @@ await AssertQuery(
             """
 SELECT s."Id", s."ArrayContainerEntityId", s."ArrayOfStringConvertedToDelimitedString", s."Byte", s."ByteArray", s."Bytea", s."EnumConvertedToInt", s."EnumConvertedToString", s."IList", s."IntArray", s."IntList", s."ListOfStringConvertedToDelimitedString", s."NonNullableText", s."NullableEnumConvertedToString", s."NullableEnumConvertedToStringWithNonNullableLambda", s."NullableIntArray", s."NullableIntList", s."NullableStringArray", s."NullableStringList", s."NullableText", s."StringArray", s."StringList", s."ValueConvertedArrayOfEnum", s."ValueConvertedListOfEnum", s."Varchar10", s."Varchar15"
 FROM "SomeEntities" AS s
-WHERE array_position(s."IntArray", 6) - 1 = 1
+WHERE COALESCE(array_position(s."IntArray", 6) - 1, -1) = 1
 """);
     }
 
@@ -849,7 +849,7 @@ await AssertQuery(
             """
 SELECT s."Id", s."ArrayContainerEntityId", s."ArrayOfStringConvertedToDelimitedString", s."Byte", s."ByteArray", s."Bytea", s."EnumConvertedToInt", s."EnumConvertedToString", s."IList", s."IntArray", s."IntList", s."ListOfStringConvertedToDelimitedString", s."NonNullableText", s."NullableEnumConvertedToString", s."NullableEnumConvertedToStringWithNonNullableLambda", s."NullableIntArray", s."NullableIntList", s."NullableStringArray", s."NullableStringList", s."NullableText", s."StringArray", s."StringList", s."ValueConvertedArrayOfEnum", s."ValueConvertedListOfEnum", s."Varchar10", s."Varchar15"
 FROM "SomeEntities" AS s
-WHERE array_position(s."IntArray", 6, 2) - 1 = 1
+WHERE COALESCE(array_position(s."IntArray", 6, 2) - 1, -1) = 1
 """);
     }
 
diff --git a/test/EFCore.PG.FunctionalTests/Query/ArrayListQueryTest.cs b/test/EFCore.PG.FunctionalTests/Query/ArrayListQueryTest.cs
index cfe968bb5d..02ef5d2a75 100644
--- a/test/EFCore.PG.FunctionalTests/Query/ArrayListQueryTest.cs
+++ b/test/EFCore.PG.FunctionalTests/Query/ArrayListQueryTest.cs
@@ -856,7 +856,7 @@ await AssertQuery(
             """
 SELECT s."Id", s."ArrayContainerEntityId", s."ArrayOfStringConvertedToDelimitedString", s."Byte", s."ByteArray", s."Bytea", s."EnumConvertedToInt", s."EnumConvertedToString", s."IList", s."IntArray", s."IntList", s."ListOfStringConvertedToDelimitedString", s."NonNullableText", s."NullableEnumConvertedToString", s."NullableEnumConvertedToStringWithNonNullableLambda", s."NullableIntArray", s."NullableIntList", s."NullableStringArray", s."NullableStringList", s."NullableText", s."StringArray", s."StringList", s."ValueConvertedArrayOfEnum", s."ValueConvertedListOfEnum", s."Varchar10", s."Varchar15"
 FROM "SomeEntities" AS s
-WHERE array_position(s."IntList", 6) - 1 = 1
+WHERE COALESCE(array_position(s."IntList", 6) - 1, -1) = 1
 """);
     }
 
@@ -872,7 +872,7 @@ await AssertQuery(
             """
 SELECT s."Id", s."ArrayContainerEntityId", s."ArrayOfStringConvertedToDelimitedString", s."Byte", s."ByteArray", s."Bytea", s."EnumConvertedToInt", s."EnumConvertedToString", s."IList", s."IntArray", s."IntList", s."ListOfStringConvertedToDelimitedString", s."NonNullableText", s."NullableEnumConvertedToString", s."NullableEnumConvertedToStringWithNonNullableLambda", s."NullableIntArray", s."NullableIntList", s."NullableStringArray", s."NullableStringList", s."NullableText", s."StringArray", s."StringList", s."ValueConvertedArrayOfEnum", s."ValueConvertedListOfEnum", s."Varchar10", s."Varchar15"
 FROM "SomeEntities" AS s
-WHERE array_position(s."IntList", 6, 2) - 1 = 1
+WHERE COALESCE(array_position(s."IntList", 6, 2) - 1, -1) = 1
 """);
     }