Picture a number that will not sit still: ten, nine, eight — each one smaller than the last, each one bringing a fixed moment closer. Countdown can be thought of as the stretch of time those shrinking numbers cover. Nothing has happened yet; that is the point. The whole feeling of the word lives in the gap between the first number and zero, and in knowing exactly where that gap ends.
The supplied Wiktionary entry gives the formation directly: countdown is count + down — counting that goes downwards, towards zero.
手上的 Wiktionary 資料直接寫著 count + down：往下數的數。數到最底就是零，也就是事情發生的那一刻，這跟今天三個用法的畫面都對得上。
Wiktionary entry for countdown, kaikki extract source_ref kaikki:3f6f69a190036ae4:328995188:27970 — etymology_text: “From count + down.”
From the picture
把倒數做成一種節目形式
同樣是往上逼近那個最重要的一刻，只是這裡走的不是秒數，是名次。節目從低名次一路播到第一名，聽眾等的就是最後揭曉的那一首，等待的形狀跟發射倒數一模一樣。
noun · B2
A radio or television show that plays the most popular songs of a week one after another, starting near the bottom of the list and ending with the number one song.
排行榜倒數節目
noun · B1
The time just before something happens — most often before a spacecraft is launched — when someone counts backwards to zero and the last checks are made.
倒數計時
noun · B1
The period before an important event, when people are waiting for it and getting more and more excited as the day comes closer.
倒數階段 / 進入倒數