diff --git a/sklearn/naive_bayes.py b/sklearn/naive_bayes.py
index 4e7345bf0f5c62e8b5a02fa6bc9624e24c5f2e35..eb29765efe7d794dd1dc809bda7f9021eb82aebd 100644
--- a/sklearn/naive_bayes.py
+++ b/sklearn/naive_bayes.py
@@ -266,9 +266,7 @@ class BaseDiscreteNB(BaseNB):
         elif self.fit_prior:
             # empirical prior, with sample_weight taken into account
             y_freq = Y.sum(axis=0)
-            eps = np.finfo(1.).eps
-            self.class_log_prior_ = (np.log(y_freq + eps)
-                                    - np.log(y_freq.sum() + eps))
+            self.class_log_prior_ = np.log(y_freq) - np.log(y_freq.sum())
         else:
             self.class_log_prior_ = np.zeros(n_classes) - np.log(n_classes)