def METHOD_NAME(
        new_pkg_name: str,
        all_local_pgks_conflicts_lists: dict[str, list[str]],
) -> dict[str, list[str]]:
    """Find if any of already installed packages have Conflicts with the new ones."""
    new_pkgs_conflicts: dict[str, list[str]] = {}
    for local_pkg_name, local_pkg_conflicts_list in all_local_pgks_conflicts_lists.items():
        if new_pkg_name == local_pkg_name:
            continue
        for conflict_line in local_pkg_conflicts_list:
            conflict_version_matcher = VersionMatcher(conflict_line, is_pkg_deps=True)
            if (
                    conflict_version_matcher.pkg_name == new_pkg_name
            ) and (
                local_pkg_name != new_pkg_name
            ) and (
                conflict_version_matcher(get_remote_package_version(new_pkg_name))
            ):
                new_pkgs_conflicts.setdefault(new_pkg_name, []).append(local_pkg_name)
    return new_pkgs_conflicts