England ended the third day with a lead of 186 runs for the loss of 7 wickets, but if they can add a few more runs in the first session of the fourth day, then they will definitely take the lead beyond 200 runs. In this case, if England can get out three or four batsmen of the India toppers while completing the lead naturally, then their chances of winning the match will definitely increase a lot. England are waiting for an opportunity where if they can bat better in the first innings and take it beyond 600 runs, then they will definitely go beyond 250 runs. England's chances of winning this Test are 80%.
You are right England start to Day 4 is key. If they can get their lead over 200 runs and quickly dismiss some of India main batsmen their chances of winning will greatly improve. It seems there was slight confusion in original text about England first innings. Real focus should be on how many more runs they can add to their current lead in their second innings. If they manage to build a lead of 200-250 runs and take early wickets they will be in very strong spot even if 80% winning chance might be bit high for Test cricket.
England are already leading by 187 runs and still have 7 wickets in hand but they have not finished their innings. Maybe they will bat for a while at the beginning of the fourth day and they will want to score 200 or more runs on the scoreboard and then they may declare the innings. If England can lead by 200 or more runs at the end of the first innings, then the chances of England winning this match will definitely increase a lot. Even with the current state of the game, I would say that the result of this match is more likely to go in England's favor, if the result does not go in England's favor then the match may still be a draw but India will not be able to win this match and India's dream of winning the series may be over here.
I think England will not declare their innings and will try to continue playing as many overs as they can and increase the score. With a lead of only 186 runs, England will not be able to compete with India. In response to India's 358 runs in the first innings, the England batsmen batted well and were able to make a challenging score, but England will want to win, as a result of which they will want to take a more lead without declaring their innings. In the current situation of the match, if England could have given a lead of 400 runs in the first innings, then there is a possibility of winning, otherwise the match is likely to be drawn. The third day's play has already ended. If the England batsmen can survive till the lunch break of the fourth day's play and give the desired target, then they will have a chance of winning.