I've always known that I'm very quick with my hands. If someone throws something, I catch it almost before I'm aware it has been thrown. It probably helps that I spent years at baseball stadiums as a child – my dad was manager of the New York Yankees. We didn't practise together, but I guess my reflexes must have naturally developed. When I was young, I had no idea how useful this skill would become.

Two summers ago, in Bay Ridge, Brooklyn, babies were on my mind. I was going to visit a friend with her newborn and was on my way to a toy store to buy a gift. I'd once lived in the neighbourhood and on a whim I decided to head back to my old haunt, a cupcake shop, for a coffee. Sitting alone at a table outside with my drink, I was approached by a typical Brooklyn older man, who in a calm and very matter-of-fact way told me to call 911, because there was a baby on a fire escape.

I jumped up to see where the baby was. I was so surprised to see it, wearing a little onesie and lying on the fire escape railings between the second and third storeys. He was lying like a cat, with his tummy on the hand rail, arms and legs tucked in. He was resting there, looking around nonchalantly. I was nervous, but the baby boy became my only priority.

As I was on the phone to the emergency services, I made eye contact with the child, keeping him calm, telling him to stay there. Some people were going up the stairs to find the parents, who were apparently sleeping through the whole drama.

I just wanted the child, who I later found out was called Dillon, to feel safe – and he didn't seem upset. He was comfortable up there, just looking down at me for nearly 10 minutes. I hoped he'd stay there until somebody could rescue him.

Apparently he had slipped through pieces of cardboard placed next to an air-conditioning unit in the window, and without bars to protect him he'd crawled out and up the fire escape towards the next storey. He was clearly a physically capable child, but he was only 16 months old. For him to even climb up and balance in that position was incredible.

Then he slipped. Instinctively, he grabbed on as he fell, so he was gripping the railing, hanging by his arms. I knew he couldn't hold on, 25 feet above the street, for long. I sensed people had gathered behind, but my attention was purely focused on my intention to catch the baby. I made sure I was positioned to save him.

I told 911 he was falling and within a minute Dillon had. As he tumbled, he hit a protruding plastic sign for a yoga shop. There were shocked gasps as everyone heard his face knock the sign and he started to cry.

I didn't move to catch him; I was in exactly the right spot. He just fell into my outstretched arms. He felt weightless. It was effortless. It felt like a basic and simple human response. Somehow I even managed to keep hold of my phone. I was in shock, and before I knew it a man stepped forward and took him from me; he worked in the local hardware store. There was blood on Dillon's face, but it turned out it was only his lip that had been cut. He stopped crying pretty quickly – he seemed very resilient. I think he should take all the credit.

The moments after he fell were overwhelming. People were being very kind and hugging me, telling me I was an angel. Dillon's parents had been woken by the commotion and his mother came down and thanked me, and his dad hugged me. I had been holding everything together, but when I caught the subway I finally let go and burst into tears. I was then able to think about my own feelings that I'd put aside and considered what would have happened if I hadn't caught him. That is when I really felt scared.

The reality of saving someone's life is intense. I play it over in my head so many times, I think it has changed me. I am calm and more at ease with things. I study mindfulness, and I see now that if we let intuition lead us, we can deal with anything. I think I was meant to be there.

• As told to Sarah Smith

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