This series is noted for the difficult situations the writers cook up for Richard Kimble to get out of but even by their standards this one seems contrived. Kimble hops a freight train only to find a woman, (Diana Hyland) with a baby on board. Police are searching every car. She says that her father sent them. Kimble seems to accept that at face value. He is, of course, primarily interested in not being caught. But he was not only a doctor but a pediatrician, (Ed Peterson's book on the series says that Quinn Martin specifically chose that discipline because it made him a humanitarian whereas other medical disciplines were more likely to produce a guy who was in the profession to get rich. Thus, Kimble could not tear himself away from situations like this.
But even after they get away, he makes no attempt to contact the authorizes over this woman who is clearly endangering her baby by hitting the road like this – until he finds out it's not her baby at all, that her baby is dead and she stole this one. Then he finally disengages, only to find the deluded woman has left the baby someplace and will only tell her 'husband', (Kimble), forcing him to return and announce himself.