Probabilistically shaped (PS) pulse amplitude modulation (PAM) is a promising technique for intra-data-center networks due to its superior performance, for which a low-complexity and cost-effective distributed matching method is critical. In this work, we propose an energy-level-assigned method to yield PS-PAM-4 signals with various bit rates based on variable probabilistic distributions. We experimentally demonstrate the proposed method in a 25 Gbaud PS-PAM-4 transmission over a bandwidth of approximately 10 GHz. Compared to a uniform PAM-4 system, the proposed multi-distributed PS-PAM-4 system approaches the hard decision threshold at a wide range of received optical power for different applications.