How does one distinguish between a mere coincidence and Baba's divine intervention? I need a clear example.

Chapter 51 provides a perfect illustration of this. Kakasaheb Dixit, who longed for Baba's darshan, happened to be at Mirikar's house when a long-hidden portrait of Sai was suddenly uncovered and given to him. The text itself calls this a 'strange coincidence.' Immediately after, Dixit and Madhavrao faced a full train, only for the guard to turn out to be an acquaintance who helped them. Finally, upon arrival, they unexpectedly met Nana Saheb Chandorkar, who was also going to Shirdi. A skeptic sees a series of lucky breaks, but the devotee understands this as the 'capable Sai' acting to fulfill a devotee's wish, weaving together events that seem like coincidences into a purposeful plan.