routing: add error case for zero capacity

Since no edge should have a zero capacity associated with it, passing a
zero capacity to the bimodal probability calculation results now in an
error.

docs/release-notes/release-notes-0.16.0.md

@@ -459,6 +459,10 @@ in the lnwire package](https://github.com/lightningnetwork/lnd/pull/7303)
   https://github.com/lightningnetwork/lnd/pull/6815)
 * [The a priori capacity factor is made configurable and its effect is 
   limited.](https://github.com/lightningnetwork/lnd/pull/7444)
+* Local edges and hop hints [are extended with a
+  capacity](https://github.com/lightningnetwork/lnd/pull/7520) to avoid channel
+  white listing in probability calculations. The influence of the node
+  probability is reduced.
 
 ## Configuration
 * Note that [this pathfinding change](https://github.com/lightningnetwork/lnd/pull/6815)

routing/probability_bimodal.go

@@ -49,6 +49,10 @@ var (
 
 	// ErrInvalidDecayTime is returned when we get a decay time below zero.
 	ErrInvalidDecayTime = errors.New("decay time must be larger than zero")
+
+	// ErrZeroCapacity is returned when we encounter a channel with zero
+	// capacity in probability estimation.
+	ErrZeroCapacity = errors.New("capacity must be larger than zero")
 )
 
 // BimodalConfig contains configuration for our probability estimator.
@@ -226,7 +230,9 @@ func (p *BimodalEstimator) directProbability(now time.Time,
 		capacity, successAmount, failAmount, amt,
 	)
 	if err != nil {
-		log.Errorf("error computing probability: %v", err)
+		log.Errorf("error computing probability to node: %v "+
+			"(node: %v, results: %v, amt: %v, capacity: %v)",
+			err, toNode, results, amt, capacity)
 
 		return 0.0
 	}
@@ -441,10 +447,10 @@ func (p *BimodalEstimator) probabilityFormula(capacityMsat, successAmountMsat,
 	failAmount := float64(failAmountMsat)
 	amount := float64(amountMsat)
 
-	// Capacity being zero is a sentinel value to ignore the probability
+	// In order for this formula to give reasonable results, we need to have
-	// estimation, we'll return the full probability here.
+	// an estimate of the capacity of a channel (or edge between nodes).
 	if capacity == 0.0 {
-		return 1.0, nil
+		return 0, ErrZeroCapacity
 	}
 
 	// We cannot send more than the capacity.

routing/probability_bimodal_test.go

@@ -232,6 +232,16 @@ func TestSuccessProbability(t *testing.T) {
 			require.NoError(t, err)
 		})
 	}
+
+	// We expect an error when the capacity is zero.
+	t.Run("zero capacity", func(t *testing.T) {
+		t.Parallel()
+
+		_, err := estimator.probabilityFormula(
+			0, 0, 0, 0,
+		)
+		require.ErrorIs(t, err, ErrZeroCapacity)
+	})
 }
 
 // TestIntegral tests certain limits of the probability distribution integral.
@@ -649,7 +659,9 @@ func FuzzProbability(f *testing.F) {
 	estimator := BimodalEstimator{
 		BimodalConfig: BimodalConfig{BimodalScaleMsat: scale},
 	}
-	f.Add(uint64(0), uint64(0), uint64(0), uint64(0))
+
+	// We don't start fuzzing at zero, because that would cause an error.
+	f.Add(uint64(1), uint64(0), uint64(0), uint64(0))
 
 	f.Fuzz(func(t *testing.T, capacity, successAmt, failAmt, amt uint64) {
 		_, err := estimator.probabilityFormula(