Four points J, K, L, and M are chosen at random on the circumference of a circle.

"Anchor" J  at any point on the  circumference

Proceeding in a clock-wise direction we could have the following possibilities for  the four points

JKLM

JKML

JLKM

JLMK

JMLK

JMKL

Note that the  two entries in red  are  the ones  where  chords JK  and LM  intersect

So.....the probability of intersecting chords  is   2 / 6    =     1 / 3