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With the exponential growth of large data produced by IoT applications and the need for lowcost computational resources, new paradigms such as volunteer cloud computing (VCC) have recently been introduced. In VCC, volunteers do not disclose resource information before joining the system. This leads to uncertainties about the level of trust in the system. The majority of available trust models are suitable for peer-to-peer (P2P) systems, which rely on direct and indirect interaction, and might cause memory consumption overhead concerns in large systems. To address this problem, this paper introduces ProTrust, a probabilistic framework that defines the trust of a host in VCC. We expand the concept of trust in VCC and develop two new metrics: (1) trustworthiness based on the priority of a task, named loyalty, and (2) trustworthiness affected by behavioral change. We first utilized a modified Beta distribution function, and the behavior of resources are classified into different loyalty levels. Then, we present a behavior detection method to reflect recent changes in behavior. We evaluated ProTrust experimentally with a real workload trace and observed that the framework's estimation of the trust score improved by approximately 15% and its memory consumption decreased by more than 65% compared to existing methods.