From data collated from UPSC prelims 2017, nearly 5.5 lakh people wrote the exam out of the 11.36 lakh people who registered. In 2017, there 980 vacancies for positions out of which around 170 were for IAS.
What is the chance of getting selected based on pure probability: 170/5.5 lakh *100 = 0.03%
As you can see, the probability to get selected for IAS vacancies is as low as 0.03% Getting selected, from a statistical point of view, is as unlikey as winning a lottery. This is why many people fail to clear IAS.