Many-core processors exhibit hundreds to thousands of cores, which can execute lots of multi-threaded tasks in parallel. Restrictive power dissipation capacity of a many-core prevents all its executing tasks from operating at their peak performance together. Furthermore, the ability of a task to exploit part of the power budget allocated to it depends upon its current execution phase. This mandates careful rationing of the power budget amongst the tasks for full exploitation of the many-core. Past research proposed power budgeting techniques that redistribute power budget amongst tasks based on up-to-date information about their current phases. This phase information needs to be constantly propagated throughout the system and processed, inhibiting scalability. In this work, we propose a novel probabilistic technique for power budgeting which requires no exchange of phase information yet provides mathematical guarantees on judicial use of the TDP. The proposed probabilistic technique reduces the power budgeting overheads by 97.13% in comparison to a non-probabilistic approach, while providing almost equal performance on simulated thousand-core system.