Part of the celebrated 'Fab Four' that also comprises Joe Root and Kane Williamson, both Kohli and Smith have endured struggles with the bat in recent times, though they have scored a century each in the first three Tests of the five-match series.
Williamson suffered a groin strain during New Zealand's innings and 154-run loss to Sri Lanka last month. He has been advised to remain at home for rehabilitation ahead of the first Test against India in Bengaluru, which begins on October 16.
In Kane's post, the caption read, 'And then there was 3. Welcome to the world, beautiful girl. So grateful for your safe arrival and the exciting journey ahead.'
Virat Kohli's world record 50th ODI hundred and a scintillating century by Shreyas Iyer powered India into the final of the World Cup with a 70-run victory over New Zealand
In the process, the Indian pacer Mohammed Shami etched his name into the record books, becoming the fastest bowler to claim 50 wickets in the ODI World Cup.
Regular skipper Williamson returned to action on Friday after nearly five months, having nursed an ACL injury, before suffering a thumb fracture against Bangladesh that ruled him out again for a few matches
The 33-year-old was absent for the tournament opener match against England and is now aiming to make a return during New Zealand's third match against Bangladesh on October 13 in Chennai.