def METHOD_NAME(distribution_json: str) -> str:
    distribution = json_to_distribution(distribution_json)
    old_distribution: BaseDistribution
    # Float distributions.
    if isinstance(distribution, FloatDistribution):
        if distribution.log:
            old_distribution = LogUniformDistribution(
                low=distribution.low,
                high=distribution.high,
            )
        else:
            if distribution.step is not None:
                old_distribution = DiscreteUniformDistribution(
                    low=distribution.low,
                    high=distribution.high,
                    q=distribution.step,
                )
            else:
                old_distribution = UniformDistribution(
                    low=distribution.low,
                    high=distribution.high,
                )
    # Integer distributions.
    elif isinstance(distribution, IntDistribution):
        if distribution.log:
            old_distribution = IntLogUniformDistribution(
                low=distribution.low,
                high=distribution.high,
                step=distribution.step,
            )
        else:
            old_distribution = IntUniformDistribution(
                low=distribution.low,
                high=distribution.high,
                step=distribution.step,
            )
    # Categorical distribution.
    else:
        old_distribution = distribution
    return distribution_to_json(old_distribution)