You are mistaken. There is absolutely no bar in applying for new job, even in probation period. Probation has no relationship with applying for new position. You only have to apply through proper channel, send an advance copy of application to the recruiting agency and seek NOC from the present department where you are working.
As a Government Officer dealing with personnel matter for a quite long time in different capacity, I am assuring you that you would not face any problem if you apply through proper channel, Also indicate your current employment status in your application, which will enable you to include your past service (i.e., present employment) in your new position, which will be beneficial for you in different service matters in future.
"If you are killed in action, you go to Heaven. If you win, you rule this Earth (as beautiful as Heaven). That is why, O son of Kunti, take a firm resolve and fight!"-- Shrimad Bhagwad Gita