にちがいない

Definitely is the case
Plain form verb + に違いない
Noun/Adjective + に違いない

に違いない is an expression meaning “There’s no mistake about it”.
It comes from 違う, meaning “different”. Turned into its ます stem, it is a noun meaning difference.
Literally the phrase mean “There’s no difference (between that and the truth).”

This phrase may also appear as に間違いない (see below), に相違ない (rare/formal) or に決まっている (more informal).

Examples

• 彼は合格するに違いない
  He will definitely pass.
  
  
• 何かあったに違いない
  Something definitely happened.
  
  
• これは大きな問題に違いない
  This is definitely a big problem.
  
  
• 彼は強いに違いない
  He’s definitely strong.
  
  
• 彼女を愛しているに違いない
  He is definitely in love with her.
  
  
• Hakushiki Japaneseは一番に違いない
  Hakushiki Japanese is definitely the best.
  
  

に間違いない

There’s no mistake about it
Plain form verb + に違いない
Noun/Adjective + に違いない

に間違いない has the same meaning and usage as にちがいない, but is a tiny bit stronger or more certain. (Source)

Examples

• 彼が犯人に間違いない
  He’s definitely the culprit
  
  
• あれはやばいに間違いない
   That’s definitely dangerous.
  
  

Comparison

• 彼に違いない
  It’s definitely him.
  
  
• 彼に間違いない
  I’m sure it’s him.
  
  
• 鉄に違いない
  Its definitely iron. (or at least close)
  
  
• 鉄に間違いない
  I’m positive its iron.