Shield Nodes of the Rogue Drone

A rogue battle-drone is protected by shield nodes, and it currently has $3$ of them active. You fire at it repeatedly, and each shot resolves in one of three ways: (a) you destroy a node but an internal backup instantly replaces it, leaving the node count exactly where it was; (b) the shot is deflected and the drone spins up one additional node; (c) you destroy a node for good, reducing the count by one. Outcomes (b) and (c) occur with equal probability; outcome (a) has some other, unspecified probability. If the node count ever drops to $0$, the drone is disabled and you win. If it ever climbs to $5$, the drone becomes untouchable and you must abort. What is the probability you disable the drone?