darou だろう used to express uncertainty

でしょう　and だろう　have the same meaning, only でしょう　is formal and だろう　is informal.

verbs
{ 食べる　/　食べた } 　だろう
{ taberu / tabeta } darou
(someone will probably eat / probably ate)

i-adjectives
{ 高い　/　高かった } 　だろう
{ takai / takakatta } darou
(something is / was probably expensive)

na-adjectives
{ 静か　/　静かだった } 　だろう
{ shizuka / shizuka datta } darou
(something is / was probably quiet)

nouns
{ 学生　/　学生だった } 　だろう
{ gakusei / gakusei datta } darou
(someone is / was probably a student)