def smoothed_estimate(n_x: int, N: int, d: int) -> float:
    """Estimates with 1-Laplace smoothing the probability of a category from a multinomial distribution.

        Args:
            n_x (int): The count of some outcome "x" among ``N`` trials.
                SHOULD be non-negative.
                SHOULD be no greater than ``N``.
            N (int): The count of trials.
                SHOULD be non-negative.
            d (int): The count of distinct possible outcomes.
                (i.e. the dimensionality of the distribution)
                SHOULD be positive.

        Returns:
            float: The estimated probability with 1-Laplace smoothing of some outcome "x".
    """
    return (n_x + 1) / (N + d)