What led to the selection of Mathias as one of the Apostles?

In an assembly of the members of the early church, Peter reminded the
people that the place of Judas, following his suicide after betraying Christ,
must be filled in fulfilment of the scriptures

Some of the conditions for
the election were that 

• the person must have witnessed the baptism of Jesus
  by John, 
• He must have been a companion of Jesus. 
•  He must have
  witnessed Jesus’ ministry on earth up to the time he was crucified, 
• The
  person must have witnessed Jesus
  resurrection.

Two men, Barnabas whose surname was Justus and Matthias were
presented for the election. The apostles prayed :r God’s guidance in the
selection, cast lots for them and the lots fell on Matthias and he was counted
among the twelve apostles.