removeProfile_(profileId) {
    const count = this.profileIds_[profileId];
    if (count > 1) {
      // Reference count will be decremented but not to zero.
      this.profileIds_[profileId]--;
    } else if (count !== undefined) {
      // Reference count would be decremented to zero (or is bogus).
      delete this.profileIds_[profileId];
      this.throttledRefresh_.start();
    }
  }
Decrement reference count for the given profile ID and update the combined
profile if it should change.

@param {string} profileId
@private