There's no availabilities column in the participant list. A participant's availability appears after you click Invite, in the panel that opens on the right:
The easiest way to schedule invites
Let the system optimise across everyone's availability instead of checking people one by one:
Select one or more suitable participants.
Click the Invite button at the top.
Click Populate suggested times.
Hit Send.
The system matches participants to session times based on all of their availabilities at once. There's a short video walkthrough of this flow (it may show an earlier interface, but the steps are the same).
Find participants available for a specific slot
If a cancellation has left a specific session time empty:
Click Filter near the top of your participant list.
Filter by Preferred times is any of the slot you want to fill.
The list narrows to participants available at that time.
Invite a handful of them to fill the slot quickly.