I downloaded Debian Live from this link:
http://cdimage.debian.org/debian-cd/current-live/amd64/iso-hybrid/debian-live-8.5.0-amd64-kde-desktop.iso
I booted into this KDE live system, opened Konsole terminal emulator, typed "ping debian.org" (as non-root) into it and saw:
"ping: icmp open socket: Operation not permitted".
"sudo ping debian.org" works.

user@debian:~$ ls -l /bin/ping
-rwxr-xr-x 1 root root 44104 Nov  8  2014 /bin/ping
user@debian:~$ stat /bin/ping
  File: ‘/bin/ping’
  Size: 44104           Blocks: 88         IO Block: 1024   regular file
Device: 13h/19d Inode: 509687      Links: 1
Access: (0755/-rwxr-xr-x)  Uid: (    0/    root)   Gid: (    0/    root)
Access: 2014-11-08 17:04:43.000000000 +0000
Modify: 2014-11-08 17:04:43.000000000 +0000
Change: 2014-11-08 17:04:43.000000000 +0000
 Birth: -

Control: reassign -1 cdimage.debian.org

ping uses Linux capabilities(7) to work as a non-suid binary. What seems
to be happening is that the initial base installation performed by
debootstrap is done on a filesystem that supports capabilities, but then
the capabilities are lost when the files are copied to the CD image
filesystem. I'm not sure if that's because the target filesystem doesn't
support capabilities or that the process of copying fails to preserve
them.

I'm re-assigning this to the cdimage.debian.org team so they can
investigate.

noah

Just tested ping with "debian-live-9.1.0-amd64-kde-desktop.iso" and
with "debian-live-9.1.0-amd64-cinnamon-desktop.iso". Ping performs
correctly on both systems.

@Asker: mind trying it again and close the bug it works for you? Thx.

Regards,
 - Darsha