diff --git a/dlib/bayes_utils/bayes_utils.h b/dlib/bayes_utils/bayes_utils.h
index 7cc617cd7..95529c26a 100644
--- a/dlib/bayes_utils/bayes_utils.h
+++ b/dlib/bayes_utils/bayes_utils.h
@@ -333,6 +333,8 @@ namespace dlib
             if (table.is_in_domain(a))
             {
                 table[a] += p;
+                if (table[a] > 1.0)
+                    table[a] = 1.0;
             }
             else
             {
diff --git a/dlib/bayes_utils/bayes_utils_abstract.h b/dlib/bayes_utils/bayes_utils_abstract.h
index a7a22fd71..e5ac77332 100644
--- a/dlib/bayes_utils/bayes_utils_abstract.h
+++ b/dlib/bayes_utils/bayes_utils_abstract.h
@@ -294,7 +294,8 @@ namespace dlib
                     - #size() == size() + 1
                     - #probability(a) == p
                 - else
-                    - #probability(a) == probability(a) + p
+                    - #probability(a) == min(probability(a) + p, 1.0)
+                      (i.e. does a saturating add)
                 - #has_entry_for(a) == true
         !*/