A seemingly chance encounter often hides a carefully arranged plan. The moment Saul and his servant enter the city, their anticipated meeting with Samuel unfolds exactly as directed by the young women they met earlier on the road. This prior interaction outside the city is not a coincidence, but rather a clear sign of future success. Throughout history, key figures such as Abraham's servant Eliezer, Jacob, and Moses all encountered young women just before entering a new place, and their journeys ultimately succeeded. For Saul, experiencing this same pattern is a subtle hint that he will soon attain the kingship [אברבנאל].
As Saul and his servant step into the town, Samuel is simultaneously leaving one of the houses and walking directly toward them [רד״ק, ביאור שטיינזלץ]. On the surface, Samuel is simply on his way up to the high place to partake in a meal, fulfilling the exact sequence of events the young women had predicted [אברבנאל, ביאור שטיינזלץ].
While this crossing of paths appears completely random, divine providence guides the routine walk. God carefully timed and directed Samuel's movements so he would step outside at the exact second needed to intersect with Saul. Ultimately, God's orchestration is the central reason behind Samuel departing at that specific time [מלבי״ם].