Trigger an automation when another automation triggers

That said, now I think I understand your use case, the second automation is irrelevant. All you need is one automation with a conditional final action…

- id: 'camerasnapshotfromstairs'
  alias: '[SYS] Stairs Camera snapshot'
  trigger: []
  condition: []
  action:
  - service: camera.snapshot
    data:
      entity_id: camera.stairs
      filename: /home/homeassistant/.homeassistant/www/images/snapshot.jpg
  - condition: state
    entity_id: group.presence_tracker
    state: 'not_home'
  - delay: 00:00:02
  - service: notify.pushbullet
    data:
      data:
        file: '/home/homeassistant/.homeassistant/www/images/snapshot.jpg'
      title: Stairs Motion Sensor Triggered
      target: device/Argy
      message: Take this snapshot of the stairs