Newcastle game with Leicester City and Chelsea won't be tough at all, this is a game they will have full points that will make them to qualify for champions league next season. Leicester City are in the relegation zone and struggling on how to win their games, Chelsea Is still a struggling team that Newcastle is fit enough to defeat. Newcastle being part of top four in the league have been sealed, I don't think they will lose their position.
Newcastle will have no problem beating Leicester, but they may face a tough game from Chelsea. You can't completely think of Chelsea as a team that is always losing when they have such quality players. Chelsea can be a stumbling block for Newcastle as they experienced when they were held to a 2-2 draw by Leeds.
But I agree that Newcastle will fight hard to secure Champions League tickets this season. Their chances are good to become representatives of the Premier League to the Champions League, so a Newcastle win is definitely much more expected than a Chelsea win unless you are a Liverpool fan.