With the increasingly deployed Wireless Local/Personal Area Network (WLAN/WPAN) devices, channel conflict has become very frequent and severe when one WLAN/WPAN technology coexists with other WLAN/WPAN technologies in the same interfering range. In this paper, we study the coexistence issue between the most prevalent WLAN and WPAN technologies, namely the IEEE 802.11b and IEEE 802.15.1 standards. We present analytical models on the non-conflicting channel allocation probabilities, focusing on the coexistence scenarios of one IEEE 802.15.1 network coexisting with one or multiple IEEE 802.11b networks. The results show that channel allocation conflicts does occur more frequently as the number of IEEE 802.11b networks increases. Moreover, the proposed analytical model in this letter is simple and applicable to other wireless technologies, as long as the channel allocation mechanisms are known.