The donkeys of Kish, Saul's father, were lost. Kish said to Saul his son, Take now one of the servants with you, and arise, go seek the donkeys.
There are a great many "chances" or "accidents," as we might call them, in this narrative, but none of them could be anything other than the providential intervention of God in human affairs in order to achieve the divine purpose.  The straying away of Kish's donkeys, Saul's futile search for them, and his "accidental" arrival at the city where Samuel was - who can believe that any of these occurrences was "by chance"?