import math


def norm_entropy(probs):
    """get the normalized entropy based on a list of proabilities

    Parameters
    ----------
    probs: list
        list of probabilities

    Returns
    -------
    normalized entropy of the probabilities
    """

    entropy = 0
    for prob in probs:
        if prob > 0:
            entropy += prob * math.log(prob, math.e)
        else:
            entropy += 0
    return - entropy / len(probs)