Probationary periods make no difference - all it means is that there isn't a notice period on either side. Even then, a one month lag isn't going to put off a company if it needs to get rid of underperforming or spare staff.On the bright side, your current firm could just as easily lay you off. Plus, if the new firm is in the market to hire (an, having done your homework, you've decided that you're happy to join them) they presumably have some confidence in their future pipeline.