Basically, a happening that re-occurs shows that it is not chance but it is its nature and so it will continue.

The Tana'im argue about whether this logic applies after 2 times or after 3 times.

The Gemara in Bava Basra 29a attempts to derive this from Shor Tam and Shor Mu'ad but does not succeed.

Some say that the source is a Halachah l'Moshe mi'Sinai, like other legal measures. See at length the Zer Zahav (2) in the Sefer Isur v'Heter ha'Aroch, chapter 41.

All the best,

Reuven Weiner